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URLhttps://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta
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Meta Titletfp.distributions.Beta | TensorFlow Probability
Meta DescriptionBeta distribution.
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Beta distribution. Inherits From: AutoCompositeTensorDistribution , Distribution , AutoCompositeTensor tfp . distributions . Beta ( concentration1 , concentration0 , validate_args = False , allow_nan_stats = True , force_probs_to_zero_outside_support = False , name = 'Beta' ) The Beta distribution is defined over the (0, 1) interval using parameters concentration1 (aka 'alpha') and concentration0 (aka 'beta'). Mathematical Details The probability density function (pdf) is, pdf(x; alpha, beta) = x**(alpha - 1) (1 - x)**(beta - 1) / Z Z = Gamma(alpha) Gamma(beta) / Gamma(alpha + beta) where: concentration1 = alpha , concentration0 = beta , Z is the normalization constant, and, Gamma is the gamma function . The concentration parameters represent mean total counts of a 1 or a 0 , i.e., concentration1 = alpha = mean * total_concentration concentration0 = beta = (1. - mean) * total_concentration where mean in (0, 1) and total_concentration is a positive real number representing a mean total_count = concentration1 + concentration0 . Distribution parameters are automatically broadcast in all functions; see examples for details. Samples of this distribution are reparameterized (pathwise differentiable). The derivatives are computed using the approach described in the paper Michael Figurnov, Shakir Mohamed, Andriy Mnih. Implicit Reparameterization Gradients, 2018 Examples import tensorflow_probability as tfp tfd = tfp . distributions # Create a batch of three Beta distributions. alpha = [ 1 , 2 , 3 ] beta = [ 1 , 2 , 3 ] dist = tfd . Beta ( alpha , beta ) dist . sample ([ 4 , 5 ]) # Shape [4, 5, 3] # `x` has three batch entries, each with two samples. x = [[ .1 , .4 , .5 ], [ .2 , .3 , .5 ]] # Calculate the probability of each pair of samples under the corresponding # distribution in `dist`. dist . prob ( x ) # Shape [2, 3] # Define an equivalent Beta distribution parameterized by `mean` and # `total_concentration`: dist = tfd . Beta . experimental_from_mean_concentration ( mean = 0.5 , total_concentration = alpha + beta ) # Create batch_shape=[2, 3] via parameter broadcast: alpha = [[ 1. ], [ 2 ]] # Shape [2, 1] beta = [ 3. , 4 , 5 ] # Shape [3] dist = tfd . Beta ( alpha , beta ) # alpha broadcast as: [[1., 1, 1,], # [2, 2, 2]] # beta broadcast as: [[3., 4, 5], # [3, 4, 5]] # batch_Shape [2, 3] dist . sample ([ 4 , 5 ]) # Shape [4, 5, 2, 3] x = [ .2 , .3 , .5 ] # x will be broadcast as [[.2, .3, .5], # [.2, .3, .5]], # thus matching batch_shape [2, 3]. dist . prob ( x ) # Shape [2, 3] Compute the gradients of samples w.r.t. the parameters: alpha = tf . constant ( 1.0 ) beta = tf . constant ( 2.0 ) dist = tfd . Beta ( alpha , beta ) samples = dist . sample ( 5 ) # Shape [5] loss = tf . reduce_mean ( tf . square ( samples )) # Arbitrary loss function # Unbiased stochastic gradients of the loss function grads = tf . gradients ( loss , [ alpha , beta ]) Args concentration1 Positive floating-point Tensor indicating mean number of successes; aka 'alpha'. concentration0 Positive floating-point Tensor indicating mean number of failures; aka 'beta'. validate_ args Python bool , default False . When True distribution parameters are checked for validity despite possibly degrading runtime performance. When False invalid inputs may silently render incorrect outputs. allow_ nan_ stats Python bool , default True . When True , statistics (e.g., mean, mode, variance) use the value ' Na N ' to indicate the result is undefined. When False , an exception is raised if one or more of the statistic's batch members are undefined. force_ probs_ to_ zero_ outside_ support If True , force prob( x) == 0 and log_prob( x) == -inf for values of x outside the distribution support. name Python str name prefixed to Ops created by this class. Attributes allow_ nan_ stats Python bool describing behavior when a stat is undefined. Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E[(X - mean)**2] is also undefined. batch_ shape Shape of a single sample from a single event index as a Tensor Shape . May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution. concentration0 Concentration parameter associated with a 0 outcome. concentration1 Concentration parameter associated with a 1 outcome. dtype The DType of Tensor s handled by this Distribution . event_ shape Shape of a single sample from a single batch as a Tensor Shape . May be partially defined or unknown. experimental_ shard_ axis_ names The list or structure of lists of active shard axis names. force_ probs_ to_ zero_ outside_ support name Name prepended to all ops created by this Distribution . name_ scope Returns a tf.name_scope instance for this class. non_ trainable_ variables Sequence of non-trainable variables owned by this module and its submodules. parameters Dictionary of parameters used to instantiate this Distribution . reparameterization_ type Describes how samples from the distribution are reparameterized. Currently this is one of the static instances tfd.FULLY_REPARAMETERIZED or tfd.NOT_REPARAMETERIZED . submodules Sequence of all sub-modules. Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on). a = tf . Module () b = tf . Module () c = tf . Module () a . b = b b . c = c list ( a . submodules ) == [ b , c ] True list ( b . submodules ) == [ c ] True list ( c . submodules ) == [] True trainable_ variables Sequence of trainable variables owned by this module and its submodules. validate_ args Python bool indicating possibly expensive checks are enabled. variables Sequence of variables owned by this module and its submodules. Methods batch_ shape_ tensor View source batch_shape_tensor ( name = 'batch_shape_tensor' ) Shape of a single sample from a single event index as a 1-D Tensor . The batch dimensions are indexes into independent, non-identical parameterizations of this distribution. Args name name to give to the op Returns batch_ shape Tensor . cdf View source cdf ( value , name = 'cdf' , ** kwargs ) Cumulative distribution function. Given random variable X , the cumulative distribution function cdf is: cdf(x) := P[X <= x] Additional documentation from Beta : Args value float or double Tensor . name Python str prepended to names of ops created by this function. **kwargs Named arguments forwarded to subclass implementation. Returns cdf a Tensor of shape sample_shape( x) + self. batch_ shape with values of type self. dtype . copy View source copy ( ** override_parameters_kwargs ) Creates a deep copy of the distribution. Args **override_ parameters_ kwargs String/value dictionary of initialization arguments to override with new values. Returns distribution A new instance of type( self) initialized from the union of self.parameters and override_parameters_kwargs, i.e., dict( self. parameters, **override_ parameters_ kwargs) . covariance View source covariance ( name = 'covariance' , ** kwargs ) Covariance. Covariance is (possibly) defined only for non-scalar-event distributions. For example, for a length- k , vector-valued distribution, it is calculated as, Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])] where Cov is a (batch of) k x k matrix, 0 <= (i, j) < k , and E denotes expectation. Alternatively, for non-vector, multivariate distributions (e.g., matrix-valued, Wishart), Covariance shall return a (batch of) matrices under some vectorization of the events, i.e., Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above] where Cov is a (batch of) k' x k' matrices, 0 <= (i, j) < k' = reduce_prod(event_shape) , and Vec is some function mapping indices of this distribution's event dimensions to indices of a length- k' vector. Args name Python str prepended to names of ops created by this function. **kwargs Named arguments forwarded to subclass implementation. Returns covariance Floating-point Tensor with shape [B1, . . . , Bn, k', k'] where the first n dimensions are batch coordinates and k' = reduce_prod( self. event_ shape) . cross_ entropy View source cross_entropy ( other , name = 'cross_entropy' ) Computes the (Shannon) cross entropy. Denote this distribution ( self ) by P and the other distribution by Q . Assuming P, Q are absolutely continuous with respect to one another and permit densities p(x) dr(x) and q(x) dr(x) , (Shannon) cross entropy is defined as: H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x) where F denotes the support of the random variable X ~ P . other types with built-in registrations: Beta Args other tfp.distributions.Distribution instance. name Python str prepended to names of ops created by this function. Returns cross_ entropy self. dtype Tensor with shape [B1, . . . , Bn] representing n different calculations of (Shannon) cross entropy. entropy View source entropy ( name = 'entropy' , ** kwargs ) Shannon entropy in nats. event_ shape_ tensor View source event_shape_tensor ( name = 'event_shape_tensor' ) Shape of a single sample from a single batch as a 1-D int32 Tensor . Args name name to give to the op Returns event_ shape Tensor . experimental_ default_ event_ space_ bijector View source experimental_default_event_space_bijector ( * args , ** kwargs ) Bijector mapping the reals (R**n) to the event space of the distribution. Distributions with continuous support may implement _default_event_space_bijector which returns a subclass of tfp.bijectors.Bijector that maps R**n to the distribution's event space. For example, the default bijector for the Beta distribution is tfp.bijectors.Sigmoid() , which maps the real line to [0, 1] , the support of the Beta distribution. The default bijector for the CholeskyLKJ distribution is tfp.bijectors.CorrelationCholesky , which maps R^(k * (k-1) // 2) to the submanifold of k x k lower triangular matrices with ones along the diagonal. The purpose of experimental_default_event_space_bijector is to enable gradient descent in an unconstrained space for Variational Inference and Hamiltonian Monte Carlo methods. Some effort has been made to choose bijectors such that the tails of the distribution in the unconstrained space are between Gaussian and Exponential. For distributions with discrete event space, or for which TFP currently lacks a suitable bijector, this function returns None . Args *args Passed to implementation _ default_ event_ space_ bijector . **kwargs Passed to implementation _ default_ event_ space_ bijector . Returns event_ space_ bijector Bijector instance or None . experimental_ fit View source @classmethod experimental_fit ( value , sample_ndims = 1 , validate_args = False , ** init_kwargs ) Instantiates a distribution that maximizes the likelihood of x . Args value a Tensor valid sample from this distribution family. sample_ ndims Positive int Tensor number of leftmost dimensions of value that index i.i.d. samples. Default value: 1 . validate_ args Python bool , default False . When True , distribution parameters are checked for validity despite possibly degrading runtime performance. When False , invalid inputs may silently render incorrect outputs. Default value: False . **init_ kwargs Additional keyword arguments passed through to cls. _ _ init_ _ . These take precedence in case of collision with the fitted parameters; for example, tfd. Normal. experimental_fit( [1. , 1. ], scale=20.) returns a Normal distribution with scale=20. rather than the maximum likelihood parameter scale=0. . Returns maximum_ likelihood_ instance instance of cls with parameters that maximize the likelihood of value . experimental_ from_ mean_ concentration View source @classmethod experimental_from_mean_concentration ( mean , total_concentration , ** kwargs ) Constructs a Beta from its mean and total concentration. Experimental: Naming, location of this API may change. Total concentration, sometimes called "sample size", is the sum of the two concentration parameters ( concentration1 and concentration0 in __init__ ). Args mean The mean of the constructed distribution. total_ concentration The sum of the two concentration parameters. Must be greater than 0. **kwargs Other keyword arguments passed directly to _ _ init_ _ , e.g. validate_ args . Returns beta A distribution with the given parameterization. experimental_ from_ mean_ variance View source @classmethod experimental_from_mean_variance ( mean , variance , ** kwargs ) Constructs a Beta from its mean and variance. Experimental: Naming, location of this API may change. Variance must be less than mean * (1. - mean) , and in particular less than the maximal variance of 0.25, which occurs with mean = 0.5 . Args mean The mean of the constructed distribution. variance The variance of the constructed distribution. **kwargs Other keyword arguments passed directly to _ _ init_ _ , e.g. validate_ args . Returns beta A distribution with the given parameterization. experimental_ local_ measure View source experimental_local_measure ( value , backward_compat = False , ** kwargs ) Returns a log probability density together with a TangentSpace . A TangentSpace allows us to calculate the correct push-forward density when we apply a transformation to a Distribution on a strict submanifold of R^n (typically via a Bijector in the TransformedDistribution subclass). The density correction uses the basis of the tangent space. Args value float or double Tensor . backward_ compat bool specifying whether to fall back to returning Full Space as the tangent space, and representing R^n with the standard basis. **kwargs Named arguments forwarded to subclass implementation. Returns log_ prob a Tensor representing the log probability density, of shape sample_shape( x) + self. batch_ shape with values of type self. dtype . tangent_ space a Tangent Space object (by default Full Space ) representing the tangent space to the manifold at value . Raises UnspecifiedTangentSpaceError if backward_ compat is False and the _ experimental_ tangent_ space attribute has not been defined. experimental_ sample_ and_ log_ prob View source experimental_sample_and_log_prob ( sample_shape = (), seed = None , name = 'sample_and_log_prob' , ** kwargs ) Samples from this distribution and returns the log density of the sample. The default implementation simply calls sample and log_prob : def _sample_and_log_prob ( self , sample_shape , seed , ** kwargs ): x = self . sample ( sample_shape = sample_shape , seed = seed , ** kwargs ) return x , self . log_prob ( x , ** kwargs ) However, some subclasses may provide more efficient and/or numerically stable implementations. Args sample_ shape integer Tensor desired shape of samples to draw. Default value: () . seed PRNG seed; see tfp.random.sanitize_seed for details. Default value: None . name name to give to the op. Default value: 'sample_ and_ log_ prob' . **kwargs Named arguments forwarded to subclass implementation. Returns samples a Tensor , or structure of Tensor s, with prepended dimensions sample_ shape . log_ prob a Tensor of shape sample_shape( x) + self. batch_ shape with values of type self. dtype . is_ scalar_ batch View source is_scalar_batch ( name = 'is_scalar_batch' ) Indicates that batch_shape == [] . Args name Python str prepended to names of ops created by this function. Returns is_ scalar_ batch bool scalar Tensor . is_ scalar_ event View source is_scalar_event ( name = 'is_scalar_event' ) Indicates that event_shape == [] . Args name Python str prepended to names of ops created by this function. Returns is_ scalar_ event bool scalar Tensor . kl_ divergence View source kl_divergence ( other , name = 'kl_divergence' ) Computes the Kullback--Leibler divergence. Denote this distribution ( self ) by p and the other distribution by q . Assuming p, q are absolutely continuous with respect to reference measure r , the KL divergence is defined as: KL[p, q] = E_p[log(p(X)/q(X))] = -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x) = H[p, q] - H[p] where F denotes the support of the random variable X ~ p , H[., .] denotes (Shannon) cross entropy, and H[.] denotes (Shannon) entropy. other types with built-in registrations: Beta Args other tfp.distributions.Distribution instance. name Python str prepended to names of ops created by this function. Returns kl_ divergence self. dtype Tensor with shape [B1, . . . , Bn] representing n different calculations of the Kullback-Leibler divergence. log_ cdf View source log_cdf ( value , name = 'log_cdf' , ** kwargs ) Log cumulative distribution function. Given random variable X , the cumulative distribution function cdf is: log_cdf(x) := Log[ P[X <= x] ] Often, a numerical approximation can be used for log_cdf(x) that yields a more accurate answer than simply taking the logarithm of the cdf when x << -1 . Additional documentation from Beta : Args value float or double Tensor . name Python str prepended to names of ops created by this function. **kwargs Named arguments forwarded to subclass implementation. Returns logcdf a Tensor of shape sample_shape( x) + self. batch_ shape with values of type self. dtype . log_ prob View source log_prob ( value , name = 'log_prob' , ** kwargs ) Log probability density/mass function. Additional documentation from Beta : Args value float or double Tensor . name Python str prepended to names of ops created by this function. **kwargs Named arguments forwarded to subclass implementation. Returns log_ prob a Tensor of shape sample_shape( x) + self. batch_ shape with values of type self. dtype . log_ survival_ function View source log_survival_function ( value , name = 'log_survival_function' , ** kwargs ) Log survival function. Given random variable X , the survival function is defined: log_survival_function(x) = Log[ P[X > x] ] = Log[ 1 - P[X <= x] ] = Log[ 1 - cdf(x) ] Typically, different numerical approximations can be used for the log survival function, which are more accurate than 1 - cdf(x) when x >> 1 . Args value float or double Tensor . name Python str prepended to names of ops created by this function. **kwargs Named arguments forwarded to subclass implementation. Returns Tensor of shape sample_shape( x) + self. batch_ shape with values of type self. dtype . mean View source mean ( name = 'mean' , ** kwargs ) Mean. mode View source mode ( name = 'mode' , ** kwargs ) Mode. Additional documentation from Beta : param_ shapes View source @classmethod param_shapes ( sample_shape , name = 'DistributionParamShapes' ) Shapes of parameters given the desired shape of a call to sample() . (deprecated) This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample() . Subclasses should override class method _param_shapes . Args sample_ shape Tensor or python list/tuple. Desired shape of a call to sample() . name name to prepend ops with. Returns dict of parameter name to Tensor shapes. param_ static_ shapes View source @classmethod param_static_shapes ( sample_shape ) param_shapes with static (i.e. TensorShape ) shapes. (deprecated) This is a class method that describes what key/value arguments are required to instantiate the given Distribution so that a particular shape is returned for that instance's call to sample() . Assumes that the sample's shape is known statically. Subclasses should override class method _param_shapes to return constant-valued tensors when constant values are fed. Args sample_ shape Tensor Shape or python list/tuple. Desired shape of a call to sample() . Returns dict of parameter name to Tensor Shape . Raises Value Error if sample_ shape is a Tensor Shape and is not fully defined. parameter_ properties View source @classmethod parameter_properties ( dtype = tf . float32 , num_classes = None ) Returns a dict mapping constructor arg names to property annotations. This dict should include an entry for each of the distribution's Tensor -valued constructor arguments. Distribution subclasses are not required to implement _parameter_properties , so this method may raise NotImplementedError . Providing a _parameter_properties implementation enables several advanced features, including: Distribution batch slicing ( sliced_distribution = distribution[i:j] ). Automatic inference of _batch_shape and _batch_shape_tensor , which must otherwise be computed explicitly. Automatic instantiation of the distribution within TFP's internal property tests. Automatic construction of 'trainable' instances of the distribution using appropriate bijectors to avoid violating parameter constraints. This enables the distribution family to be used easily as a surrogate posterior in variational inference. In the future, parameter property annotations may enable additional functionality; for example, returning Distribution instances from tf.vectorized_map . Args dtype Optional float dtype to assume for continuous-valued parameters. Some constraining bijectors require advance knowledge of the dtype because certain constants (e.g., tfb. Softplus. low ) must be instantiated with the same dtype as the values to be transformed. num_ classes Optional int Tensor number of classes to assume when inferring the shape of parameters for categorical-like distributions. Otherwise ignored. Returns parameter_ properties A str -> tfp.python.internal.parameter_properties.ParameterProperties dict mapping constructor argument names to ParameterProperties` instances. Raises Not Implemented Error if the distribution class does not implement _ parameter_ properties . prob View source prob ( value , name = 'prob' , ** kwargs ) Probability density/mass function. Additional documentation from Beta : Args value float or double Tensor . name Python str prepended to names of ops created by this function. **kwargs Named arguments forwarded to subclass implementation. Returns prob a Tensor of shape sample_shape( x) + self. batch_ shape with values of type self. dtype . quantile View source quantile ( value , name = 'quantile' , ** kwargs ) Quantile function. Aka 'inverse cdf' or 'percent point function'. Given random variable X and p in [0, 1] , the quantile is: quantile(p) := x such that P[X <= x] == p Args value float or double Tensor . name Python str prepended to names of ops created by this function. **kwargs Named arguments forwarded to subclass implementation. Returns quantile a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype . sample View source sample ( sample_shape = (), seed = None , name = 'sample' , ** kwargs ) Generate samples of the specified shape. Note that a call to sample() without arguments will generate a single sample. Args sample_shape 0D or 1D int32 Tensor . Shape of the generated samples. seed PRNG seed; see tfp.random.sanitize_seed for details. name name to give to the op. **kwargs Named arguments forwarded to subclass implementation. Returns samples a Tensor with prepended dimensions sample_shape . stddev View source stddev ( name = 'stddev' , ** kwargs ) Standard deviation. Standard deviation is defined as, stddev = E[(X - E[X])**2]**0.5 where X is the random variable associated with this distribution, E denotes expectation, and stddev.shape = batch_shape + event_shape . Args name Python str prepended to names of ops created by this function. **kwargs Named arguments forwarded to subclass implementation. Returns stddev Floating-point Tensor with shape identical to batch_shape + event_shape , i.e., the same shape as self.mean() . survival_function View source survival_function ( value , name = 'survival_function' , ** kwargs ) Survival function. Given random variable X , the survival function is defined: survival_function(x) = P[X > x] = 1 - P[X <= x] = 1 - cdf(x). Args value float or double Tensor . name Python str prepended to names of ops created by this function. **kwargs Named arguments forwarded to subclass implementation. Returns Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype . unnormalized_log_prob View source unnormalized_log_prob ( value , name = 'unnormalized_log_prob' , ** kwargs ) Potentially unnormalized log probability density/mass function. This function is similar to log_prob , but does not require that the return value be normalized. (Normalization here refers to the total integral of probability being one, as it should be by definition for any probability distribution.) This is useful, for example, for distributions where the normalization constant is difficult or expensive to compute. By default, this simply calls log_prob . Args value float or double Tensor . name Python str prepended to names of ops created by this function. **kwargs Named arguments forwarded to subclass implementation. Returns unnormalized_log_prob a Tensor of shape sample_shape(x) + self.batch_shape with values of type self.dtype . variance View source variance ( name = 'variance' , ** kwargs ) Variance. Variance is defined as, Var = E[(X - E[X])**2] where X is the random variable associated with this distribution, E denotes expectation, and Var.shape = batch_shape + event_shape . Args name Python str prepended to names of ops created by this function. **kwargs Named arguments forwarded to subclass implementation. Returns variance Floating-point Tensor with shape identical to batch_shape + event_shape , i.e., the same shape as self.mean() . with_name_scope @classmethod with_name_scope ( method ) Decorator to automatically enter the module name scope. class MyModule ( tf . Module ): @tf . Module . with_name_scope def __call__ ( self , x ): if not hasattr ( self , 'w' ): self . w = tf . Variable ( tf . random . normal ([ x . shape [ 1 ], 3 ])) return tf . matmul ( x , self . w ) Using the above module would produce tf.Variable s and tf.Tensor s whose names included the module name: mod = MyModule () mod ( tf . ones ([ 1 , 2 ])) < tf . Tensor : shape = ( 1 , 3 ), dtype = float32 , numpy =... , dtype = float32 ) > mod . w < tf . Variable 'my_module/Variable:0' shape = ( 2 , 3 ) dtype = float32 , numpy =... , dtype = float32 ) > Args method The method to wrap. Returns The original method wrapped such that it enters the module's name scope. __getitem__ View source __getitem__ ( slices ) Slices the batch axes of this distribution, returning a new instance. b = tfd . Bernoulli ( logits = tf . zeros ([ 3 , 5 , 7 , 9 ])) b . batch_shape # => [3, 5, 7, 9] b2 = b [:, tf . newaxis , ... , - 2 :, 1 :: 2 ] b2 . batch_shape # => [3, 1, 5, 2, 4] x = tf . random . normal ([ 5 , 3 , 2 , 2 ]) cov = tf . matmul ( x , x , transpose_b = True ) chol = tf . linalg . cholesky ( cov ) loc = tf . random . normal ([ 4 , 1 , 3 , 1 ]) mvn = tfd . MultivariateNormalTriL ( loc , chol ) mvn . batch_shape # => [4, 5, 3] mvn . event_shape # => [2] mvn2 = mvn [:, 3 :, ... , :: - 1 , tf . newaxis ] mvn2 . batch_shape # => [4, 2, 3, 1] mvn2 . event_shape # => [2] Args slices slices from the [] operator Returns dist A new tfd.Distribution instance with sliced parameters. __iter__ View source __iter__ ()
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[Install](https://www.tensorflow.org/install) - [Learn](https://www.tensorflow.org/learn) - More - [API](https://www.tensorflow.org/api) - More - [Resources](https://www.tensorflow.org/resources) - More - [Overview](https://www.tensorflow.org/probability) - [Guide & Tutorials](https://www.tensorflow.org/probability/overview) - [API](https://www.tensorflow.org/probability/api_docs/python/tfp) - [Community](https://www.tensorflow.org/community) - More - [Why TensorFlow](https://www.tensorflow.org/about) - More - [GitHub](https://github.com/tensorflow) - tfp - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp) - tfp. bijectors - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors) - [AbsoluteValue](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/AbsoluteValue) - [Ascending](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Ascending) - [AutoCompositeTensorBijector](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/AutoCompositeTensorBijector) - [AutoregressiveNetwork](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/AutoregressiveNetwork) - [BatchNormalization](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/BatchNormalization) - [Bijector](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Bijector) - [Blockwise](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Blockwise) - [Chain](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Chain) - [CholeskyOuterProduct](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/CholeskyOuterProduct) - [CholeskyToInvCholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/CholeskyToInvCholesky) - [Composition](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Composition) - [CorrelationCholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/CorrelationCholesky) - [Cumsum](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Cumsum) - [DiscreteCosineTransform](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/DiscreteCosineTransform) - [Exp](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Exp) - [Expm1](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Expm1) - [FFJORD](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/FFJORD) - [FillScaleTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/FillScaleTriL) - [FillTriangular](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/FillTriangular) - [FrechetCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/FrechetCDF) - [GeneralizedExtremeValueCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/GeneralizedExtremeValueCDF) - [GeneralizedPareto](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/GeneralizedPareto) - [Glow](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Glow) - [GlowDefaultExitNetwork](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/GlowDefaultExitNetwork) - [GlowDefaultNetwork](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/GlowDefaultNetwork) - [GompertzCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/GompertzCDF) - [GumbelCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/GumbelCDF) - [Householder](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Householder) - [Identity](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Identity) - [Inline](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Inline) - [Invert](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Invert) - [IteratedSigmoidCentered](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/IteratedSigmoidCentered) - [JointMap](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/JointMap) - [KumaraswamyCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/KumaraswamyCDF) - [LambertWTail](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/LambertWTail) - [Log](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Log) - [Log1p](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Log1p) - [MaskedAutoregressiveFlow](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/MaskedAutoregressiveFlow) - [MatrixInverseTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/MatrixInverseTriL) - [MatvecLU](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/MatvecLU) - [MoyalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/MoyalCDF) - [NormalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/NormalCDF) - [Pad](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Pad) - [Permute](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Permute) - [Power](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Power) - [PowerTransform](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/PowerTransform) - [RationalQuadraticSpline](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/RationalQuadraticSpline) - [RayleighCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/RayleighCDF) - [RealNVP](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/RealNVP) - [Reciprocal](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Reciprocal) - [Reshape](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Reshape) - [Restructure](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Restructure) - [Scale](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Scale) - [ScaleMatvecDiag](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/ScaleMatvecDiag) - [ScaleMatvecLU](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/ScaleMatvecLU) - [ScaleMatvecLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/ScaleMatvecLinearOperator) - [ScaleMatvecLinearOperatorBlock](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/ScaleMatvecLinearOperatorBlock) - [ScaleMatvecTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/ScaleMatvecTriL) - [Shift](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Shift) - [ShiftedGompertzCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/ShiftedGompertzCDF) - [Sigmoid](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Sigmoid) - [Sinh](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Sinh) - [SinhArcsinh](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/SinhArcsinh) - [SoftClip](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/SoftClip) - [Softfloor](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Softfloor) - [SoftmaxCentered](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/SoftmaxCentered) - [Softplus](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Softplus) - [Softsign](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Softsign) - [Split](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Split) - [Square](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Square) - [Tanh](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Tanh) - [TransformDiagonal](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/TransformDiagonal) - [Transpose](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Transpose) - [UnitVector](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/UnitVector) - [WeibullCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/WeibullCDF) - [masked\_autoregressive\_default\_template](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/masked_autoregressive_default_template) - [masked\_dense](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/masked_dense) - [pack\_sequence\_as](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/pack_sequence_as) - [real\_nvp\_default\_template](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/real_nvp_default_template) - [tree\_flatten](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/tree_flatten) - tfp. debugging - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/debugging) - benchmarking - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/debugging/benchmarking) - [BenchmarkTfFunctionConfig](https://www.tensorflow.org/probability/api_docs/python/tfp/debugging/benchmarking/BenchmarkTfFunctionConfig) - [benchmark\_tf\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/debugging/benchmarking/benchmark_tf_function) - [default\_benchmark\_config](https://www.tensorflow.org/probability/api_docs/python/tfp/debugging/benchmarking/default_benchmark_config) - tfp. distributions - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions) - [Auto Composite Tensor Distribution](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/AutoCompositeTensorDistribution) - [Autoregressive](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Autoregressive) - [Batch Broadcast](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/BatchBroadcast) - [Batch Reshape](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/BatchReshape) - [Bates](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Bates) - [Bernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Bernoulli) - [Beta](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta) - [Beta Binomial](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/BetaBinomial) - [Beta Quotient](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/BetaQuotient) - [Binomial](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Binomial) - [Blockwise](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Blockwise) - [Categorical](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Categorical) - [Cauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Cauchy) - [Chi](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Chi) - [Chi2](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Chi2) - [Cholesky LKJ](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/CholeskyLKJ) - [Determinantal Point Process](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/DeterminantalPointProcess) - [Deterministic](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Deterministic) - [Dirichlet](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Dirichlet) - [Dirichlet Multinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/DirichletMultinomial) - [Distribution](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution) - [Doublesided Maxwell](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/DoublesidedMaxwell) - [Empirical](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Empirical) - [Exp Gamma](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/ExpGamma) - [Exp Inverse Gamma](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/ExpInverseGamma) - [Exp Relaxed One Hot Categorical](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/ExpRelaxedOneHotCategorical) - [Exponential](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Exponential) - [Exponentially Modified Gaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/ExponentiallyModifiedGaussian) - [Finite Discrete](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/FiniteDiscrete) - [Gamma](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Gamma) - [Gamma Gamma](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/GammaGamma) - [Gaussian Process](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/GaussianProcess) - [Gaussian Process Regression Model](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/GaussianProcessRegressionModel) - [Generalized Extreme Value](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/GeneralizedExtremeValue) - [Generalized Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/GeneralizedNormal) - [Generalized Pareto](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/GeneralizedPareto) - [Geometric](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Geometric) - [Gumbel](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Gumbel) - [Half Cauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/HalfCauchy) - [Half Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/HalfNormal) - [Half Student T](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/HalfStudentT) - [Hidden Markov Model](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/HiddenMarkovModel) - [Horseshoe](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Horseshoe) - [Independent](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Independent) - [Inflated](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Inflated) - [Inverse Gamma](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/InverseGamma) - [Inverse Gaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/InverseGaussian) - [Johnson SU](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JohnsonSU) - [Joint Distribution](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistribution) - [Joint Distribution. Root](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistribution/Root) - [Joint Distribution Coroutine](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistributionCoroutine) - [Joint Distribution Coroutine Auto Batched](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistributionCoroutineAutoBatched) - [Joint Distribution Named](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistributionNamed) - [Joint Distribution Named Auto Batched](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistributionNamedAutoBatched) - [Joint Distribution Sequential](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistributionSequential) - [Joint Distribution Sequential Auto Batched](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistributionSequentialAutoBatched) - [Kumaraswamy](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Kumaraswamy) - [LKJ](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/LKJ) - [Lambert WDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/LambertWDistribution) - [Lambert WNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/LambertWNormal) - [Laplace](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Laplace) - [Linear Gaussian State Space Model](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/LinearGaussianStateSpaceModel) - [Log Logistic](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/LogLogistic) - [Log Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/LogNormal) - [Logistic](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Logistic) - [Logit Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/LogitNormal) - [Markov Chain](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MarkovChain) - [Masked](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Masked) - [Matrix Normal Linear Operator](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MatrixNormalLinearOperator) - [Matrix TLinear Operator](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MatrixTLinearOperator) - [Mixture](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Mixture) - [Mixture Same Family](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MixtureSameFamily) - [Moyal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Moyal) - [Multinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Multinomial) - [Multivariate Normal Diag](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MultivariateNormalDiag) - [Multivariate Normal Diag Plus Low Rank](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MultivariateNormalDiagPlusLowRank) - [Multivariate Normal Diag Plus Low Rank Covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MultivariateNormalDiagPlusLowRankCovariance) - [Multivariate Normal Full Covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MultivariateNormalFullCovariance) - [Multivariate Normal Linear Operator](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MultivariateNormalLinearOperator) - [Multivariate Normal Tri L](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MultivariateNormalTriL) - [Multivariate Student TLinear Operator](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MultivariateStudentTLinearOperator) - [Negative Binomial](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/NegativeBinomial) - [Noncentral Chi2](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/NoncentralChi2) - [Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Normal) - [Normal Inverse Gaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/NormalInverseGaussian) - [One Hot Categorical](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/OneHotCategorical) - [Ordered Logistic](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/OrderedLogistic) - [PERT](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/PERT) - [Pareto](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Pareto) - [Pixel CNN](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/PixelCNN) - [Plackett Luce](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/PlackettLuce) - [Poisson](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Poisson) - [Poisson Log Normal Quadrature Compound](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/PoissonLogNormalQuadratureCompound) - [Power Spherical](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/PowerSpherical) - [Probit Bernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/ProbitBernoulli) - [Quantized Distribution](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/QuantizedDistribution) - [Register KL](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/RegisterKL) - [Relaxed Bernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/RelaxedBernoulli) - [Relaxed One Hot Categorical](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/RelaxedOneHotCategorical) - [Reparameterization Type](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/ReparameterizationType) - [Sample](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Sample) - [Sigmoid Beta](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/SigmoidBeta) - [Sinh Arcsinh](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/SinhArcsinh) - [Skellam](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Skellam) - [Spherical Uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/SphericalUniform) - [Stopping Ratio Logistic](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/StoppingRatioLogistic) - [Student T](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/StudentT) - [Student TProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/StudentTProcess) - [Student TProcess Regression Model](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/StudentTProcessRegressionModel) - [Transformed Distribution](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/TransformedDistribution) - [Triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Triangular) - [Truncated Cauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/TruncatedCauchy) - [Truncated Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/TruncatedNormal) - [Two Piece Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/TwoPieceNormal) - [Two Piece Student T](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/TwoPieceStudentT) - [Uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Uniform) - [Variational Gaussian Process](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/VariationalGaussianProcess) - [Vector Deterministic](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/VectorDeterministic) - [Von Mises](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/VonMises) - [Von Mises Fisher](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/VonMisesFisher) - [Weibull](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Weibull) - [Wishart Linear Operator](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/WishartLinearOperator) - [Wishart Tri L](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/WishartTriL) - [Zero Inflated Negative Binomial](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/ZeroInflatedNegativeBinomial) - [Zipf](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Zipf) - [independent\_ joint\_ distribution\_ from\_ structure](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/independent_joint_distribution_from_structure) - [kl\_ divergence](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/kl_divergence) - [mvn\_ conjugate\_ linear\_ update](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/mvn_conjugate_linear_update) - [normal\_ conjugates\_ known\_ scale\_ posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/normal_conjugates_known_scale_posterior) - [normal\_ conjugates\_ known\_ scale\_ predictive](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/normal_conjugates_known_scale_predictive) - [quadrature\_ scheme\_ lognormal\_ gauss\_ hermite](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/quadrature_scheme_lognormal_gauss_hermite) - [quadrature\_ scheme\_ lognormal\_ quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/quadrature_scheme_lognormal_quantiles) - tfp. experimental - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental) - [AutoCompositeTensor](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/AutoCompositeTensor) - [as\_composite](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/as_composite) - [auto\_composite\_tensor](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_composite_tensor) - [register\_composite](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/register_composite) - auto\_batching - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching) - [Context](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/Context) - [NumpyBackend](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/NumpyBackend) - [TensorFlowBackend](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/TensorFlowBackend) - [TensorType](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/TensorType) - [Type](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/Type) - [truthy](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/truthy) - allocation\_strategy - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/allocation_strategy) - [optimize](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/allocation_strategy/optimize) - dsl - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/dsl) - [ProgramBuilder](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/dsl/ProgramBuilder) - frontend - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend) - gast\_util - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend/gast_util) - [Module](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend/gast_util/Module) - [Name](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend/gast_util/Name) - [Str](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend/gast_util/Str) - [is\_constant](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend/gast_util/is_constant) - [is\_ellipsis](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend/gast_util/is_ellipsis) - [is\_literal](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend/gast_util/is_literal) - instructions - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions) - [Block](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/Block) - [BranchOp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/BranchOp) - [ControlFlowGraph](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/ControlFlowGraph) - [Function](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/Function) - [FunctionCallOp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/FunctionCallOp) - [GotoOp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/GotoOp) - [IndirectGotoOp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/IndirectGotoOp) - [PopOp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/PopOp) - [PrimOp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/PrimOp) - [Program](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/Program) - [PushGotoOp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/PushGotoOp) - [VariableAllocation](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/VariableAllocation) - [extract\_referenced\_variables](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/extract_referenced_variables) - [halt\_op](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/halt_op) - [interpret](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/interpret) - [push\_op](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/push_op) - liveness - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/liveness) - [liveness\_analysis](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/liveness/liveness_analysis) - lowering - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/lowering) - [lower\_function\_calls](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/lowering/lower_function_calls) - numpy\_backend - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/numpy_backend) - stack\_optimization - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/stack_optimization) - [fuse\_pop\_push](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/stack_optimization/fuse_pop_push) - stackless - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/stackless) - [ExecutionQueue](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/stackless/ExecutionQueue) - [execute](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/stackless/execute) - [is\_running](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/stackless/is_running) - tf\_backend - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/tf_backend) - type\_inference - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/type_inference) - [infer\_types](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/type_inference/infer_types) - [infer\_types\_from\_signature](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/type_inference/infer_types_from_signature) - [is\_inferring](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/type_inference/is_inferring) - [signature](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/type_inference/signature) - [type\_of\_pattern](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/type_inference/type_of_pattern) - virtual\_machine - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/virtual_machine) - [execute](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/virtual_machine/execute) - [is\_staging](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/virtual_machine/is_staging) - xla - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/xla) - [compile\_nested\_output](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/xla/compile_nested_output) - bayesopt - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt) - acquisition - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition) - [AcquisitionFunction](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/AcquisitionFunction) - [GaussianProcessExpectedImprovement](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/GaussianProcessExpectedImprovement) - [GaussianProcessMaxValueEntropySearch](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/GaussianProcessMaxValueEntropySearch) - [GaussianProcessProbabilityOfImprovement](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/GaussianProcessProbabilityOfImprovement) - [GaussianProcessUpperConfidenceBound](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/GaussianProcessUpperConfidenceBound) - [MCMCReducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/MCMCReducer) - [ParallelExpectedImprovement](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/ParallelExpectedImprovement) - [ParallelProbabilityOfImprovement](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/ParallelProbabilityOfImprovement) - [ParallelUpperConfidenceBound](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/ParallelUpperConfidenceBound) - [StudentTProcessExpectedImprovement](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/StudentTProcessExpectedImprovement) - [WeightedPowerScalarization](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/WeightedPowerScalarization) - bijectors - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors) - [HighwayFlow](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors/HighwayFlow) - [ScalarFunctionWithInferredInverse](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors/ScalarFunctionWithInferredInverse) - [Sharded](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors/Sharded) - [build\_trainable\_highway\_flow](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors/build_trainable_highway_flow) - [forward\_log\_det\_jacobian\_ratio](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors/forward_log_det_jacobian_ratio) - [inverse\_log\_det\_jacobian\_ratio](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors/inverse_log_det_jacobian_ratio) - [make\_distribution\_bijector](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors/make_distribution_bijector) - distribute - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute) - [JointDistributionCoroutine](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute/JointDistributionCoroutine) - [JointDistributionNamed](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute/JointDistributionNamed) - [JointDistributionSequential](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute/JointDistributionSequential) - [Sharded](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute/Sharded) - [make\_pbroadcast\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute/make_pbroadcast_function) - [make\_psum\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute/make_psum_function) - [make\_sharded\_log\_prob\_parts](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute/make_sharded_log_prob_parts) - distributions - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions) - [ImportanceResample](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/ImportanceResample) - [IncrementLogProb](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/IncrementLogProb) - [JointDistributionPinned](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/JointDistributionPinned) - [MultiTaskGaussianProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/MultiTaskGaussianProcess) - [MultiTaskGaussianProcessRegressionModel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/MultiTaskGaussianProcessRegressionModel) - [MultivariateNormalPrecisionFactorLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/MultivariateNormalPrecisionFactorLinearOperator) - [inflated\_factory](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/inflated_factory) - [log\_prob\_ratio](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/log_prob_ratio) - marginal\_fns - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns) - [make\_backoff\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/make_backoff_cholesky) - [make\_cholesky\_like\_marginal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/make_cholesky_like_marginal_fn) - [make\_eigh\_marginal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/make_eigh_marginal_fn) - [retrying\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/retrying_cholesky) - mvn\_linear\_operator - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/mvn_linear_operator) - ps - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps) - [abs](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/abs) - [add](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/add) - [argmax](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/argmax) - [argmin](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/argmin) - [argsort](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/argsort) - [broadcast\_shape](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/broadcast_shape) - [broadcast\_to](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/broadcast_to) - [case](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/case) - [cast](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/cast) - [ceil](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/ceil) - [concat](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/concat) - [cond](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/cond) - [constant](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/constant) - [convert\_to\_shape\_tensor](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/convert_to_shape_tensor) - [cumprod](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/cumprod) - [cumsum](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/cumsum) - [dimension\_size](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dimension_size) - [equal](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/equal) - [expand\_dims](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/expand_dims) - [expm1](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/expm1) - [eye](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/eye) - [fill](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/fill) - [floor](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/floor) - [gather](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/gather) - [greater](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/greater) - [identity](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/identity) - [invert\_permutation](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/invert_permutation) - [is\_finite](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/is_finite) - [is\_inf](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/is_inf) - [is\_nan](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/is_nan) - [is\_numpy](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/is_numpy) - [less](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/less) - [linspace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/linspace) - [log](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/log) - [log1p](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/log1p) - [logical\_and](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/logical_and) - [logical\_not](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/logical_not) - [logical\_or](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/logical_or) - [maximum](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/maximum) - [minimum](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/minimum) - [nextafter](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/nextafter) - [non\_negative\_axis](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/non_negative_axis) - [not\_equal](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/not_equal) - [one\_hot](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/one_hot) - [ones](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/ones) - [ones\_like](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/ones_like) - [pad](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/pad) - [pow](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/pow) - [range](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/range) - [rank](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/rank) - [rank\_from\_shape](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/rank_from_shape) - [reduce\_all](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reduce_all) - [reduce\_any](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reduce_any) - [reduce\_max](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reduce_max) - [reduce\_min](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reduce_min) - [reduce\_prod](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reduce_prod) - [reduce\_sum](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reduce_sum) - [repeat](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/repeat) - [reshape](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reshape) - [reverse](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reverse) - [round](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/round) - [rsqrt](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/rsqrt) - [setdiff1d](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/setdiff1d) - [shape](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/shape) - [shape\_slice](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/shape_slice) - [size](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/size) - [size0](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/size0) - [slice](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/slice) - [smart\_where](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/smart_where) - [sort](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/sort) - [split](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/split) - [sqrt](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/sqrt) - [stack](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/stack) - [tensor\_scatter\_nd\_add](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensor_scatter_nd_add) - [tensor\_scatter\_nd\_sub](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensor_scatter_nd_sub) - [tensor\_scatter\_nd\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensor_scatter_nd_update) - [tile](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tile) - [top\_k](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/top_k) - [unique](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/unique) - [unstack](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/unstack) - [where](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/where) - [zeros](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/zeros) - [zeros\_like](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/zeros_like) - dtype\_util - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util) - [as\_numpy\_dtype](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/as_numpy_dtype) - [assert\_same\_float\_dtype](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/assert_same_float_dtype) - [base\_dtype](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/base_dtype) - [base\_equal](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/base_equal) - [common\_dtype](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/common_dtype) - [eps](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/eps) - [is\_bool](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/is_bool) - [is\_complex](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/is_complex) - [is\_floating](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/is_floating) - [is\_integer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/is_integer) - [is\_numpy\_compatible](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/is_numpy_compatible) - [max](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/max) - [min](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/min) - [name](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/name) - [real\_dtype](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/real_dtype) - [size](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/size) - tensorshape\_util - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util) - [as\_list](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/as_list) - [assert\_has\_rank](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/assert_has_rank) - [assert\_is\_compatible\_with](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/assert_is_compatible_with) - [concatenate](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/concatenate) - [constant\_value\_as\_shape](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/constant_value_as_shape) - [dims](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/dims) - [is\_compatible\_with](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/is_compatible_with) - [is\_fully\_defined](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/is_fully_defined) - [merge\_with](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/merge_with) - [num\_elements](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/num_elements) - [rank](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/rank) - [set\_shape](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/set_shape) - [with\_rank](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/with_rank) - [with\_rank\_at\_least](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/with_rank_at_least) - tfp\_custom\_gradient - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/tfp_custom_gradient) - [custom\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/tfp_custom_gradient/custom_gradient) - [is\_valid\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/tfp_custom_gradient/is_valid_gradient) - [prevent\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/tfp_custom_gradient/prevent_gradient) - joint\_distribution\_layers - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers) - [Affine](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/Affine) - [AffineLayer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/AffineLayer) - [Conv2D](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/Conv2D) - [Lambda](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/Lambda) - [Sequential](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/Sequential) - [SequentialLayer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/SequentialLayer) - [make\_conv2d\_layer\_class](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/make_conv2d_layer_class) - [make\_lambda\_layer\_class](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/make_lambda_layer_class) - linalg - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/linalg) - [LinearOperatorInterpolatedPSDKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/linalg/LinearOperatorInterpolatedPSDKernel) - [LinearOperatorPSDKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/linalg/LinearOperatorPSDKernel) - [LinearOperatorRowBlock](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/linalg/LinearOperatorRowBlock) - [LinearOperatorUnitary](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/linalg/LinearOperatorUnitary) - [no\_pivot\_ldl](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/linalg/no_pivot_ldl) - [simple\_robustified\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/linalg/simple_robustified_cholesky) - marginalize - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/marginalize) - [MarginalizableJointDistributionCoroutine](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/marginalize/MarginalizableJointDistributionCoroutine) - [logeinsumexp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/marginalize/logeinsumexp) - math - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math) - [exp\_pade\_4\_4](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math/exp_pade_4_4) - [expm1\_pade\_4\_4](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math/expm1_pade_4_4) - [log1p\_pade\_4\_4](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math/log1p_pade_4_4) - [log\_pade\_4\_4](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math/log_pade_4_4) - [patch\_manual\_special\_functions](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math/patch_manual_special_functions) - [reduce\_logsumexp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math/reduce_logsumexp) - [softplus](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math/softplus) - mcmc - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc) - [CovarianceReducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/CovarianceReducer) - [DiagonalMassMatrixAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/DiagonalMassMatrixAdaptation) - [EllipticalSliceSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/EllipticalSliceSampler) - [ExpectationsReducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/ExpectationsReducer) - [GradientBasedTrajectoryLengthAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/GradientBasedTrajectoryLengthAdaptation) - [GradientBasedTrajectoryLengthAdaptationResults](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/GradientBasedTrajectoryLengthAdaptationResults) - [KernelBuilder](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/KernelBuilder) - [KernelOutputs](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/KernelOutputs) - [NoUTurnSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/NoUTurnSampler) - [PotentialScaleReductionReducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/PotentialScaleReductionReducer) - [PreconditionedHamiltonianMonteCarlo](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/PreconditionedHamiltonianMonteCarlo) - [PreconditionedNoUTurnSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/PreconditionedNoUTurnSampler) - [ProgressBarReducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/ProgressBarReducer) - [Reducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/Reducer) - [SNAPERHamiltonianMonteCarlo](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/SNAPERHamiltonianMonteCarlo) - [SNAPERHamiltonianMonteCarloResults](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/SNAPERHamiltonianMonteCarloResults) - [SampleDiscardingKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/SampleDiscardingKernel) - [SampleSNAPERHamiltonianMonteCarloResults](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/SampleSNAPERHamiltonianMonteCarloResults) - [SequentialMonteCarlo](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/SequentialMonteCarlo) - [SequentialMonteCarloResults](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/SequentialMonteCarloResults) - [Sharded](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/Sharded) - [StateWithHistory](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/StateWithHistory) - [ThinningKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/ThinningKernel) - [TracingReducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/TracingReducer) - [VarianceReducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/VarianceReducer) - [WeightedParticles](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/WeightedParticles) - [WithReductions](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/WithReductions) - [WithReductionsKernelResults](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/WithReductionsKernelResults) - [augment\_prior\_with\_state\_history](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/augment_prior_with_state_history) - [augment\_with\_observation\_history](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/augment_with_observation_history) - [augment\_with\_state\_history](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/augment_with_state_history) - [chees\_criterion](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/chees_criterion) - [chees\_rate\_criterion](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/chees_rate_criterion) - [default\_make\_hmc\_kernel\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/default_make_hmc_kernel_fn) - [ess\_below\_threshold](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/ess_below_threshold) - [gen\_make\_hmc\_kernel\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/gen_make_hmc_kernel_fn) - [gen\_make\_transform\_hmc\_kernel\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/gen_make_transform_hmc_kernel_fn) - [infer\_trajectories](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/infer_trajectories) - [init\_near\_unconstrained\_zero](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/init_near_unconstrained_zero) - [log\_ess\_from\_log\_weights](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/log_ess_from_log_weights) - [make\_rwmh\_kernel\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/make_rwmh_kernel_fn) - [make\_tqdm\_progress\_bar\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/make_tqdm_progress_bar_fn) - [particle\_filter](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/particle_filter) - [reconstruct\_trajectories](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/reconstruct_trajectories) - [remc\_thermodynamic\_integrals](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/remc_thermodynamic_integrals) - [resample\_deterministic\_minimum\_error](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/resample_deterministic_minimum_error) - [resample\_independent](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/resample_independent) - [resample\_stratified](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/resample_stratified) - [resample\_systematic](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/resample_systematic) - [retry\_init](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/retry_init) - [sample\_chain](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/sample_chain) - [sample\_chain\_with\_burnin](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/sample_chain_with_burnin) - [sample\_fold](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/sample_fold) - [sample\_sequential\_monte\_carlo](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/sample_sequential_monte_carlo) - [sample\_snaper\_hmc](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/sample_snaper_hmc) - [simple\_heuristic\_tuning](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/simple_heuristic_tuning) - [snaper\_criterion](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/snaper_criterion) - [step\_kernel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/step_kernel) - [windowed\_adaptive\_hmc](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/windowed_adaptive_hmc) - [windowed\_adaptive\_nuts](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/windowed_adaptive_nuts) - nn - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn) - [Affine](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/Affine) - [AffineVariationalFlipout](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/AffineVariationalFlipout) - [AffineVariationalReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/AffineVariationalReparameterization) - [AffineVariationalReparameterizationLocal](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/AffineVariationalReparameterizationLocal) - [Convolution](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/Convolution) - [ConvolutionTranspose](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionTranspose) - [ConvolutionTransposeVariationalFlipout](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionTransposeVariationalFlipout) - [ConvolutionTransposeVariationalReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionTransposeVariationalReparameterization) - [ConvolutionV2](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionV2) - [ConvolutionVariationalFlipout](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionVariationalFlipout) - [ConvolutionVariationalFlipoutV2](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionVariationalFlipoutV2) - [ConvolutionVariationalReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionVariationalReparameterization) - [ConvolutionVariationalReparameterizationV2](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionVariationalReparameterizationV2) - [Layer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/Layer) - [Sequential](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/Sequential) - [VariationalLayer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/VariationalLayer) - initializers - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/initializers) - [glorot\_normal](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/initializers/glorot_normal) - [glorot\_uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/initializers/glorot_uniform) - [he\_normal](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/initializers/he_normal) - [he\_uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/initializers/he_uniform) - losses - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/losses) - [compute\_extra\_loss](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/losses/compute_extra_loss) - [kl\_divergence\_exact](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/losses/kl_divergence_exact) - [kl\_divergence\_monte\_carlo](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/losses/kl_divergence_monte_carlo) - [negloglik](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/losses/negloglik) - util - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util) - [CallOnce](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/CallOnce) - [RandomVariable](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/RandomVariable) - [batchify\_op](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/batchify_op) - [display\_imgs](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/display_imgs) - [expand\_dims](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/expand_dims) - [flatten\_rightmost](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/flatten_rightmost) - [halflife\_decay](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/halflife_decay) - [im2row](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/im2row) - [im2row\_index](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/im2row_index) - [make\_convolution\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_convolution_fn) - [make\_convolution\_transpose\_fn\_with\_dilation](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_convolution_transpose_fn_with_dilation) - [make\_convolution\_transpose\_fn\_with\_subkernels](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_convolution_transpose_fn_with_subkernels) - [make\_convolution\_transpose\_fn\_with\_subkernels\_matrix](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_convolution_transpose_fn_with_subkernels_matrix) - [make\_fit\_op](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_fit_op) - [make\_kernel\_bias](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_kernel_bias) - [make\_kernel\_bias\_posterior\_mvn\_diag](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_kernel_bias_posterior_mvn_diag) - [make\_kernel\_bias\_prior\_spike\_and\_slab](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_kernel_bias_prior_spike_and_slab) - [prepare\_conv\_args](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/prepare_conv_args) - [prepare\_tuple\_argument](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/prepare_tuple_argument) - [tfcompile](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/tfcompile) - [trace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/trace) - [tune\_dataset](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/tune_dataset) - [variables\_load](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/variables_load) - [variables\_save](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/variables_save) - [variables\_summary](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/variables_summary) - parallel\_filter - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/parallel_filter) - [kalman\_filter](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/parallel_filter/kalman_filter) - [sample\_walk](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/parallel_filter/sample_walk) - psd\_kernels - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels) - [AdditiveKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels/AdditiveKernel) - [ContinuousAndCategoricalValues](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels/ContinuousAndCategoricalValues) - [FeatureScaledWithCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels/FeatureScaledWithCategorical) - [FeatureScaledWithEmbeddedCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels/FeatureScaledWithEmbeddedCategorical) - [Independent](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels/Independent) - [MultiTaskKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels/MultiTaskKernel) - [Separable](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels/Separable) - sequential - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential) - [EnsembleKalmanFilterState](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/EnsembleKalmanFilterState) - [IteratedFilter](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/IteratedFilter) - [ensemble\_adjustment\_kalman\_filter\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/ensemble_adjustment_kalman_filter_update) - [ensemble\_kalman\_filter\_log\_marginal\_likelihood](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/ensemble_kalman_filter_log_marginal_likelihood) - [ensemble\_kalman\_filter\_predict](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/ensemble_kalman_filter_predict) - [ensemble\_kalman\_filter\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/ensemble_kalman_filter_update) - [extended\_kalman\_filter](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/extended_kalman_filter) - [geometric\_cooling\_schedule](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/geometric_cooling_schedule) - [inflate\_by\_scaled\_identity\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/inflate_by_scaled_identity_fn) - stats - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/stats) - [RunningCentralMoments](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/stats/RunningCentralMoments) - [RunningCovariance](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/stats/RunningCovariance) - [RunningMean](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/stats/RunningMean) - [RunningPotentialScaleReduction](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/stats/RunningPotentialScaleReduction) - [RunningVariance](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/stats/RunningVariance) - sts\_gibbs - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sts_gibbs) - [GibbsSamplerState](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sts_gibbs/GibbsSamplerState) - [build\_model\_for\_gibbs\_fitting](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sts_gibbs/build_model_for_gibbs_fitting) - [fit\_with\_gibbs\_sampling](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sts_gibbs/fit_with_gibbs_sampling) - [get\_seasonal\_latents\_shape](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sts_gibbs/get_seasonal_latents_shape) - [one\_step\_predictive](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sts_gibbs/one_step_predictive) - substrates - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/substrates) - tangent\_spaces - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces) - [AxisAlignedSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/AxisAlignedSpace) - [ConstantDiagonalSymmetricMatrixSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/ConstantDiagonalSymmetricMatrixSpace) - [FullSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/FullSpace) - [GeneralSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/GeneralSpace) - [ProbabilitySimplexSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/ProbabilitySimplexSpace) - [SphericalSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/SphericalSpace) - [SymmetricMatrixSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/SymmetricMatrixSpace) - [TangentSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/TangentSpace) - [UnspecifiedTangentSpaceError](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/UnspecifiedTangentSpaceError) - [ZeroSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/ZeroSpace) - util - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/util) - [DeferredModule](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/util/DeferredModule) - [JitPublicMethods](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/util/JitPublicMethods) - [make\_trainable](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/util/make_trainable) - [make\_trainable\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/util/make_trainable_stateless) - vi - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi) - [build\_affine\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_affine_surrogate_posterior) - [build\_affine\_surrogate\_posterior\_from\_base\_distribution](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_affine_surrogate_posterior_from_base_distribution) - [build\_affine\_surrogate\_posterior\_from\_base\_distribution\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_affine_surrogate_posterior_from_base_distribution_stateless) - [build\_affine\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_affine_surrogate_posterior_stateless) - [build\_asvi\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_asvi_surrogate_posterior) - [build\_asvi\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_asvi_surrogate_posterior_stateless) - [build\_factored\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_factored_surrogate_posterior) - [build\_factored\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_factored_surrogate_posterior_stateless) - [build\_split\_flow\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_split_flow_surrogate_posterior) - util - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/util) - [build\_linear\_operator\_zeros](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/util/build_linear_operator_zeros) - [build\_trainable\_linear\_operator\_block](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/util/build_trainable_linear_operator_block) - [build\_trainable\_linear\_operator\_diag](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/util/build_trainable_linear_operator_diag) - [build\_trainable\_linear\_operator\_full\_matrix](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/util/build_trainable_linear_operator_full_matrix) - [build\_trainable\_linear\_operator\_tril](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/util/build_trainable_linear_operator_tril) - tfp. glm - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/glm) - [Bernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/Bernoulli) - [BernoulliNormalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/BernoulliNormalCDF) - [Binomial](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/Binomial) - [CustomExponentialFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/CustomExponentialFamily) - [ExponentialFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/ExponentialFamily) - [GammaExp](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/GammaExp) - [GammaSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/GammaSoftplus) - [LogNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/LogNormal) - [LogNormalSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/LogNormalSoftplus) - [NegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/NegativeBinomial) - [NegativeBinomialSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/NegativeBinomialSoftplus) - [Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/Normal) - [NormalReciprocal](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/NormalReciprocal) - [Poisson](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/Poisson) - [PoissonSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/PoissonSoftplus) - [compute\_predicted\_linear\_response](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/compute_predicted_linear_response) - [convergence\_criteria\_small\_relative\_norm\_weights\_change](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/convergence_criteria_small_relative_norm_weights_change) - [fit](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/fit) - [fit\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/fit_one_step) - [fit\_sparse](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/fit_sparse) - [fit\_sparse\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/fit_sparse_one_step) - tfp. layers - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers) - [AutoregressiveTransform](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/AutoregressiveTransform) - [BlockwiseInitializer](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/BlockwiseInitializer) - [CategoricalMixtureOfOneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/CategoricalMixtureOfOneHotCategorical) - [Convolution1DFlipout](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/Convolution1DFlipout) - [Convolution1DReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/Convolution1DReparameterization) - [Convolution2DFlipout](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/Convolution2DFlipout) - [Convolution2DReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/Convolution2DReparameterization) - [Convolution3DFlipout](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/Convolution3DFlipout) - [Convolution3DReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/Convolution3DReparameterization) - [DenseFlipout](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/DenseFlipout) - [DenseLocalReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/DenseLocalReparameterization) - [DenseReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/DenseReparameterization) - [DenseVariational](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/DenseVariational) - [DistributionLambda](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/DistributionLambda) - [IndependentBernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/IndependentBernoulli) - [IndependentLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/IndependentLogistic) - [IndependentNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/IndependentNormal) - [IndependentPoisson](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/IndependentPoisson) - [KLDivergenceAddLoss](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/KLDivergenceAddLoss) - [KLDivergenceRegularizer](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/KLDivergenceRegularizer) - [MixtureLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/MixtureLogistic) - [MixtureNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/MixtureNormal) - [MixtureSameFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/MixtureSameFamily) - [MultivariateNormalTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/MultivariateNormalTriL) - [OneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/OneHotCategorical) - [VariableLayer](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/VariableLayer) - [VariationalGaussianProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/VariationalGaussianProcess) - [default\_loc\_scale\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/default_loc_scale_fn) - [default\_mean\_field\_normal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/default_mean_field_normal_fn) - [default\_multivariate\_normal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/default_multivariate_normal_fn) - conv\_variational - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/conv_variational) - dense\_variational - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/dense_variational) - dense\_variational\_v2 - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/dense_variational_v2) - kullback\_leibler - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/dense_variational_v2/kullback_leibler) - [augment\_kl\_xent\_docs](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/dense_variational_v2/kullback_leibler/augment_kl_xent_docs) - distribution\_layer - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/distribution_layer) - initializers - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/initializers) - masked\_autoregressive - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/masked_autoregressive) - util - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/util) - [deserialize\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/util/deserialize_function) - [serialize\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/util/serialize_function) - variable\_input - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/variable_input) - weight\_norm - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/weight_norm) - [WeightNorm](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/weight_norm/WeightNorm) - tfp. math - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/math) - [MinimizeTraceableQuantities](https://www.tensorflow.org/probability/api_docs/python/tfp/math/MinimizeTraceableQuantities) - [atan\_difference](https://www.tensorflow.org/probability/api_docs/python/tfp/math/atan_difference) - [batch\_interp\_rectilinear\_nd\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/math/batch_interp_rectilinear_nd_grid) - [batch\_interp\_regular\_1d\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/math/batch_interp_regular_1d_grid) - [batch\_interp\_regular\_nd\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/math/batch_interp_regular_nd_grid) - [bessel\_iv\_ratio](https://www.tensorflow.org/probability/api_docs/python/tfp/math/bessel_iv_ratio) - [bessel\_ive](https://www.tensorflow.org/probability/api_docs/python/tfp/math/bessel_ive) - [bessel\_kve](https://www.tensorflow.org/probability/api_docs/python/tfp/math/bessel_kve) - [betainc](https://www.tensorflow.org/probability/api_docs/python/tfp/math/betainc) - [betaincinv](https://www.tensorflow.org/probability/api_docs/python/tfp/math/betaincinv) - [bracket\_root](https://www.tensorflow.org/probability/api_docs/python/tfp/math/bracket_root) - [cholesky\_concat](https://www.tensorflow.org/probability/api_docs/python/tfp/math/cholesky_concat) - [cholesky\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/math/cholesky_update) - [clip\_by\_value\_preserve\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/math/clip_by_value_preserve_gradient) - [custom\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/math/custom_gradient) - [dawsn](https://www.tensorflow.org/probability/api_docs/python/tfp/math/dawsn) - [dense\_to\_sparse](https://www.tensorflow.org/probability/api_docs/python/tfp/math/dense_to_sparse) - [diag\_jacobian](https://www.tensorflow.org/probability/api_docs/python/tfp/math/diag_jacobian) - [erfcinv](https://www.tensorflow.org/probability/api_docs/python/tfp/math/erfcinv) - [erfcx](https://www.tensorflow.org/probability/api_docs/python/tfp/math/erfcx) - [fill\_triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/math/fill_triangular) - [fill\_triangular\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/math/fill_triangular_inverse) - [find\_root\_chandrupatla](https://www.tensorflow.org/probability/api_docs/python/tfp/math/find_root_chandrupatla) - [find\_root\_secant](https://www.tensorflow.org/probability/api_docs/python/tfp/math/find_root_secant) - [gram\_schmidt](https://www.tensorflow.org/probability/api_docs/python/tfp/math/gram_schmidt) - [hpsd\_logdet](https://www.tensorflow.org/probability/api_docs/python/tfp/math/hpsd_logdet) - [hpsd\_quadratic\_form\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/math/hpsd_quadratic_form_solve) - [hpsd\_quadratic\_form\_solvevec](https://www.tensorflow.org/probability/api_docs/python/tfp/math/hpsd_quadratic_form_solvevec) - [hpsd\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/math/hpsd_solve) - [hpsd\_solvevec](https://www.tensorflow.org/probability/api_docs/python/tfp/math/hpsd_solvevec) - [igammacinv](https://www.tensorflow.org/probability/api_docs/python/tfp/math/igammacinv) - [igammainv](https://www.tensorflow.org/probability/api_docs/python/tfp/math/igammainv) - [interp\_regular\_1d\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/math/interp_regular_1d_grid) - [lambertw](https://www.tensorflow.org/probability/api_docs/python/tfp/math/lambertw) - [lambertw\_winitzki\_approx](https://www.tensorflow.org/probability/api_docs/python/tfp/math/lambertw_winitzki_approx) - [lbeta](https://www.tensorflow.org/probability/api_docs/python/tfp/math/lbeta) - [log1mexp](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log1mexp) - [log1psquare](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log1psquare) - [log\_add\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_add_exp) - [log\_bessel\_ive](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_bessel_ive) - [log\_bessel\_kve](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_bessel_kve) - [log\_combinations](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_combinations) - [log\_cosh](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_cosh) - [log\_cumsum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_cumsum_exp) - [log\_gamma\_correction](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_gamma_correction) - [log\_gamma\_difference](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_gamma_difference) - [log\_sub\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_sub_exp) - [logerfc](https://www.tensorflow.org/probability/api_docs/python/tfp/math/logerfc) - [logerfcx](https://www.tensorflow.org/probability/api_docs/python/tfp/math/logerfcx) - [low\_rank\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/math/low_rank_cholesky) - [lu\_matrix\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/math/lu_matrix_inverse) - [lu\_reconstruct](https://www.tensorflow.org/probability/api_docs/python/tfp/math/lu_reconstruct) - [lu\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/math/lu_solve) - [minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/math/minimize) - [minimize\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/math/minimize_stateless) - [owens\_t](https://www.tensorflow.org/probability/api_docs/python/tfp/math/owens_t) - [pivoted\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/math/pivoted_cholesky) - [reduce\_kahan\_sum](https://www.tensorflow.org/probability/api_docs/python/tfp/math/reduce_kahan_sum) - [reduce\_log\_harmonic\_mean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/math/reduce_log_harmonic_mean_exp) - [reduce\_logmeanexp](https://www.tensorflow.org/probability/api_docs/python/tfp/math/reduce_logmeanexp) - [reduce\_weighted\_logsumexp](https://www.tensorflow.org/probability/api_docs/python/tfp/math/reduce_weighted_logsumexp) - [round\_exponential\_bump\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/math/round_exponential_bump_function) - [scan\_associative](https://www.tensorflow.org/probability/api_docs/python/tfp/math/scan_associative) - [secant\_root](https://www.tensorflow.org/probability/api_docs/python/tfp/math/secant_root) - [smootherstep](https://www.tensorflow.org/probability/api_docs/python/tfp/math/smootherstep) - [soft\_sorting\_matrix](https://www.tensorflow.org/probability/api_docs/python/tfp/math/soft_sorting_matrix) - [soft\_threshold](https://www.tensorflow.org/probability/api_docs/python/tfp/math/soft_threshold) - [softplus\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/math/softplus_inverse) - [sparse\_or\_dense\_matmul](https://www.tensorflow.org/probability/api_docs/python/tfp/math/sparse_or_dense_matmul) - [sparse\_or\_dense\_matvecmul](https://www.tensorflow.org/probability/api_docs/python/tfp/math/sparse_or_dense_matvecmul) - [sqrt1pm1](https://www.tensorflow.org/probability/api_docs/python/tfp/math/sqrt1pm1) - [trapz](https://www.tensorflow.org/probability/api_docs/python/tfp/math/trapz) - [value\_and\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/math/value_and_gradient) - hypergeometric - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/math/hypergeometric) - [hyp2f1\_small\_argument](https://www.tensorflow.org/probability/api_docs/python/tfp/math/hypergeometric/hyp2f1_small_argument) - ode - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/math/ode) - [BDF](https://www.tensorflow.org/probability/api_docs/python/tfp/math/ode/BDF) - [ChosenBySolver](https://www.tensorflow.org/probability/api_docs/python/tfp/math/ode/ChosenBySolver) - [Diagnostics](https://www.tensorflow.org/probability/api_docs/python/tfp/math/ode/Diagnostics) - [DormandPrince](https://www.tensorflow.org/probability/api_docs/python/tfp/math/ode/DormandPrince) - [Results](https://www.tensorflow.org/probability/api_docs/python/tfp/math/ode/Results) - [Solver](https://www.tensorflow.org/probability/api_docs/python/tfp/math/ode/Solver) - psd\_kernels - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels) - [AutoCompositeTensorPsdKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/AutoCompositeTensorPsdKernel) - [ChangePoint](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/ChangePoint) - [Constant](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/Constant) - [ExpSinSquared](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/ExpSinSquared) - [ExponentialCurve](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/ExponentialCurve) - [ExponentiatedQuadratic](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/ExponentiatedQuadratic) - [FeatureScaled](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/FeatureScaled) - [FeatureTransformed](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/FeatureTransformed) - [GammaExponential](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/GammaExponential) - [GeneralizedMatern](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/GeneralizedMatern) - [KumaraswamyTransformed](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/KumaraswamyTransformed) - [Linear](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/Linear) - [MaternFiveHalves](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/MaternFiveHalves) - [MaternOneHalf](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/MaternOneHalf) - [MaternThreeHalves](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/MaternThreeHalves) - [Parabolic](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/Parabolic) - [PointwiseExponential](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/PointwiseExponential) - [Polynomial](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/Polynomial) - [PositiveSemidefiniteKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/PositiveSemidefiniteKernel) - [RationalQuadratic](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/RationalQuadratic) - [SchurComplement](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/SchurComplement) - [SpectralMixture](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/SpectralMixture) - tfp. mcmc - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc) - [CheckpointableStatesAndTrace](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/CheckpointableStatesAndTrace) - [DualAveragingStepSizeAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/DualAveragingStepSizeAdaptation) - [HamiltonianMonteCarlo](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/HamiltonianMonteCarlo) - [MetropolisAdjustedLangevinAlgorithm](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/MetropolisAdjustedLangevinAlgorithm) - [MetropolisHastings](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/MetropolisHastings) - [NoUTurnSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/NoUTurnSampler) - [RandomWalkMetropolis](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/RandomWalkMetropolis) - [ReplicaExchangeMC](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/ReplicaExchangeMC) - [SimpleStepSizeAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/SimpleStepSizeAdaptation) - [SliceSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/SliceSampler) - [StatesAndTrace](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/StatesAndTrace) - [TransformedTransitionKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/TransformedTransitionKernel) - [TransitionKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/TransitionKernel) - [UncalibratedHamiltonianMonteCarlo](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/UncalibratedHamiltonianMonteCarlo) - [UncalibratedLangevin](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/UncalibratedLangevin) - [UncalibratedRandomWalk](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/UncalibratedRandomWalk) - [default\_swap\_proposal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/default_swap_proposal_fn) - [effective\_sample\_size](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/effective_sample_size) - [even\_odd\_swap\_proposal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/even_odd_swap_proposal_fn) - [make\_simple\_step\_size\_update\_policy](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/make_simple_step_size_update_policy) - [potential\_scale\_reduction](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/potential_scale_reduction) - [random\_walk\_normal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/random_walk_normal_fn) - [random\_walk\_uniform\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/random_walk_uniform_fn) - [sample\_annealed\_importance\_chain](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/sample_annealed_importance_chain) - [sample\_chain](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/sample_chain) - [sample\_halton\_sequence](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/sample_halton_sequence) - tfp. monte\_ carlo - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/monte_carlo) - [expectation](https://www.tensorflow.org/probability/api_docs/python/tfp/monte_carlo/expectation) - tfp. optimizer - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer) - [StochasticGradientLangevinDynamics](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/StochasticGradientLangevinDynamics) - [VariationalSGD](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/VariationalSGD) - [bfgs\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/bfgs_minimize) - [converged\_all](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/converged_all) - [converged\_any](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/converged_any) - [differential\_evolution\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/differential_evolution_minimize) - [differential\_evolution\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/differential_evolution_one_step) - [lbfgs\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/lbfgs_minimize) - [nelder\_mead\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/nelder_mead_minimize) - [nelder\_mead\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/nelder_mead_one_step) - [proximal\_hessian\_sparse\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/proximal_hessian_sparse_minimize) - [proximal\_hessian\_sparse\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/proximal_hessian_sparse_one_step) - convergence\_criteria - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/convergence_criteria) - [ConvergenceCriterion](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/convergence_criteria/ConvergenceCriterion) - [LossNotDecreasing](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/convergence_criteria/LossNotDecreasing) - [SuccessiveGradientsAreUncorrelated](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/convergence_criteria/SuccessiveGradientsAreUncorrelated) - linesearch - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/linesearch) - [hager\_zhang](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/linesearch/hager_zhang) - tfp. random - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/random) - [rademacher](https://www.tensorflow.org/probability/api_docs/python/tfp/random/rademacher) - [rayleigh](https://www.tensorflow.org/probability/api_docs/python/tfp/random/rayleigh) - [sanitize\_seed](https://www.tensorflow.org/probability/api_docs/python/tfp/random/sanitize_seed) - [spherical\_uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/random/spherical_uniform) - [split\_seed](https://www.tensorflow.org/probability/api_docs/python/tfp/random/split_seed) - tfp. stats - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/stats) - [assign\_log\_moving\_mean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/assign_log_moving_mean_exp) - [assign\_moving\_mean\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/assign_moving_mean_variance) - [auto\_correlation](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/auto_correlation) - [brier\_decomposition](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/brier_decomposition) - [brier\_score](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/brier_score) - [cholesky\_covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/cholesky_covariance) - [correlation](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/correlation) - [count\_integers](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/count_integers) - [covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/covariance) - [cumulative\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/cumulative_variance) - [expected\_calibration\_error](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/expected_calibration_error) - [expected\_calibration\_error\_quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/expected_calibration_error_quantiles) - [find\_bins](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/find_bins) - [histogram](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/histogram) - [kendalls\_tau](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/kendalls_tau) - [log\_average\_probs](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/log_average_probs) - [log\_loomean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/log_loomean_exp) - [log\_loosum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/log_loosum_exp) - [log\_soomean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/log_soomean_exp) - [log\_soosum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/log_soosum_exp) - [moving\_mean\_variance\_zero\_debiased](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/moving_mean_variance_zero_debiased) - [percentile](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/percentile) - [quantile\_auc](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/quantile_auc) - [quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/quantiles) - [stddev](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/stddev) - [variance](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/variance) - [windowed\_mean](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/windowed_mean) - [windowed\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/windowed_variance) - tfp. sts - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/sts) - [AdditiveStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/AdditiveStateSpaceModel) - [Autoregressive](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/Autoregressive) - [AutoregressiveIntegratedMovingAverage](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/AutoregressiveIntegratedMovingAverage) - [AutoregressiveMovingAverageStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/AutoregressiveMovingAverageStateSpaceModel) - [AutoregressiveStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/AutoregressiveStateSpaceModel) - [ConstrainedSeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/ConstrainedSeasonalStateSpaceModel) - [DynamicLinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/DynamicLinearRegression) - [DynamicLinearRegressionStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/DynamicLinearRegressionStateSpaceModel) - [IntegratedStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/IntegratedStateSpaceModel) - [LinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/LinearRegression) - [LocalLevel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/LocalLevel) - [LocalLevelStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/LocalLevelStateSpaceModel) - [LocalLinearTrend](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/LocalLinearTrend) - [LocalLinearTrendStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/LocalLinearTrendStateSpaceModel) - [MaskedTimeSeries](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/MaskedTimeSeries) - [MissingValuesTolerance](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/MissingValuesTolerance) - [Seasonal](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/Seasonal) - [SeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/SeasonalStateSpaceModel) - [SemiLocalLinearTrend](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/SemiLocalLinearTrend) - [SemiLocalLinearTrendStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/SemiLocalLinearTrendStateSpaceModel) - [SmoothSeasonal](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/SmoothSeasonal) - [SmoothSeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/SmoothSeasonalStateSpaceModel) - [SparseLinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/SparseLinearRegression) - [StructuralTimeSeries](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/StructuralTimeSeries) - [Sum](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/Sum) - [build\_factored\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/build_factored_surrogate_posterior) - [build\_factored\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/build_factored_surrogate_posterior_stateless) - [decompose\_by\_component](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/decompose_by_component) - [decompose\_forecast\_by\_component](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/decompose_forecast_by_component) - [fit\_with\_hmc](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/fit_with_hmc) - [forecast](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/forecast) - [impute\_missing\_values](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/impute_missing_values) - [moments\_of\_masked\_time\_series](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/moments_of_masked_time_series) - [one\_step\_predictive](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/one_step_predictive) - [regularize\_series](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/regularize_series) - [sample\_uniform\_initial\_state](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/sample_uniform_initial_state) - tfp. substrates - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates) - jax - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax) - bijectors - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors) - [AbsoluteValue](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/AbsoluteValue) - [Ascending](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Ascending) - [AutoCompositeTensorBijector](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/AutoCompositeTensorBijector) - [AutoregressiveNetwork](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/AutoregressiveNetwork) - [Bijector](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Bijector) - [Blockwise](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Blockwise) - [Chain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Chain) - [CholeskyOuterProduct](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/CholeskyOuterProduct) - [CholeskyToInvCholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/CholeskyToInvCholesky) - [Composition](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Composition) - [CorrelationCholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/CorrelationCholesky) - [Cumsum](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Cumsum) - [Exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Exp) - [Expm1](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Expm1) - [FFJORD](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/FFJORD) - [FillScaleTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/FillScaleTriL) - [FillTriangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/FillTriangular) - [FrechetCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/FrechetCDF) - [GeneralizedExtremeValueCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/GeneralizedExtremeValueCDF) - [GeneralizedPareto](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/GeneralizedPareto) - [GompertzCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/GompertzCDF) - [GumbelCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/GumbelCDF) - [Householder](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Householder) - [Identity](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Identity) - [Inline](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Inline) - [Invert](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Invert) - [IteratedSigmoidCentered](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/IteratedSigmoidCentered) - [JointMap](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/JointMap) - [KumaraswamyCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/KumaraswamyCDF) - [LambertWTail](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/LambertWTail) - [Log](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Log) - [Log1p](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Log1p) - [MaskedAutoregressiveFlow](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/MaskedAutoregressiveFlow) - [MatrixInverseTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/MatrixInverseTriL) - [MatvecLU](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/MatvecLU) - [MoyalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/MoyalCDF) - [NormalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/NormalCDF) - [Pad](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Pad) - [Permute](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Permute) - [Power](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Power) - [PowerTransform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/PowerTransform) - [RationalQuadraticSpline](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/RationalQuadraticSpline) - [RayleighCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/RayleighCDF) - [RealNVP](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/RealNVP) - [Reciprocal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Reciprocal) - [Reshape](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Reshape) - [Restructure](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Restructure) - [Scale](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Scale) - [ScaleMatvecDiag](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/ScaleMatvecDiag) - [ScaleMatvecLU](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/ScaleMatvecLU) - [ScaleMatvecLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/ScaleMatvecLinearOperator) - [ScaleMatvecLinearOperatorBlock](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/ScaleMatvecLinearOperatorBlock) - [ScaleMatvecTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/ScaleMatvecTriL) - [Shift](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Shift) - [ShiftedGompertzCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/ShiftedGompertzCDF) - [Sigmoid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Sigmoid) - [Sinh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Sinh) - [SinhArcsinh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/SinhArcsinh) - [SoftClip](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/SoftClip) - [Softfloor](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Softfloor) - [SoftmaxCentered](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/SoftmaxCentered) - [Softplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Softplus) - [Softsign](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Softsign) - [Split](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Split) - [Square](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Square) - [Tanh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Tanh) - [TransformDiagonal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/TransformDiagonal) - [Transpose](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Transpose) - [UnitVector](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/UnitVector) - [WeibullCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/WeibullCDF) - [masked\_autoregressive\_default\_template](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/masked_autoregressive_default_template) - [masked\_dense](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/masked_dense) - [pack\_sequence\_as](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/pack_sequence_as) - [real\_nvp\_default\_template](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/real_nvp_default_template) - [tree\_flatten](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/tree_flatten) - distributions - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions) - [AutoCompositeTensorDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/AutoCompositeTensorDistribution) - [Autoregressive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Autoregressive) - [BatchBroadcast](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/BatchBroadcast) - [BatchReshape](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/BatchReshape) - [Bates](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Bates) - [Bernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Bernoulli) - [Beta](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Beta) - [BetaBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/BetaBinomial) - [BetaQuotient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/BetaQuotient) - [Binomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Binomial) - [Blockwise](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Blockwise) - [Categorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Categorical) - [Cauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Cauchy) - [Chi](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Chi) - [Chi2](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Chi2) - [CholeskyLKJ](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/CholeskyLKJ) - [DeterminantalPointProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/DeterminantalPointProcess) - [Deterministic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Deterministic) - [Dirichlet](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Dirichlet) - [DirichletMultinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/DirichletMultinomial) - [Distribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Distribution) - [DoublesidedMaxwell](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/DoublesidedMaxwell) - [Empirical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Empirical) - [ExpGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/ExpGamma) - [ExpInverseGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/ExpInverseGamma) - [ExpRelaxedOneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/ExpRelaxedOneHotCategorical) - [Exponential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Exponential) - [ExponentiallyModifiedGaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/ExponentiallyModifiedGaussian) - [FiniteDiscrete](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/FiniteDiscrete) - [Gamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Gamma) - [GammaGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/GammaGamma) - [GaussianProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/GaussianProcess) - [GaussianProcessRegressionModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/GaussianProcessRegressionModel) - [GeneralizedExtremeValue](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/GeneralizedExtremeValue) - [GeneralizedNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/GeneralizedNormal) - [GeneralizedPareto](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/GeneralizedPareto) - [Geometric](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Geometric) - [Gumbel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Gumbel) - [HalfCauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/HalfCauchy) - [HalfNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/HalfNormal) - [HalfStudentT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/HalfStudentT) - [HiddenMarkovModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/HiddenMarkovModel) - [Horseshoe](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Horseshoe) - [Independent](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Independent) - [Inflated](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Inflated) - [InverseGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/InverseGamma) - [InverseGaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/InverseGaussian) - [JohnsonSU](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JohnsonSU) - [JointDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistribution) - [JointDistribution.Root](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistribution/Root) - [JointDistributionCoroutine](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistributionCoroutine) - [JointDistributionCoroutineAutoBatched](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistributionCoroutineAutoBatched) - [JointDistributionNamed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistributionNamed) - [JointDistributionNamedAutoBatched](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistributionNamedAutoBatched) - [JointDistributionSequential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistributionSequential) - [JointDistributionSequentialAutoBatched](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistributionSequentialAutoBatched) - [Kumaraswamy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Kumaraswamy) - [LKJ](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/LKJ) - [LambertWDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/LambertWDistribution) - [LambertWNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/LambertWNormal) - [Laplace](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Laplace) - [LinearGaussianStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/LinearGaussianStateSpaceModel) - [LogLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/LogLogistic) - [LogNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/LogNormal) - [Logistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Logistic) - [LogitNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/LogitNormal) - [MarkovChain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MarkovChain) - [Masked](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Masked) - [MatrixNormalLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MatrixNormalLinearOperator) - [MatrixTLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MatrixTLinearOperator) - [Mixture](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Mixture) - [MixtureSameFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MixtureSameFamily) - [Moyal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Moyal) - [Multinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Multinomial) - [MultivariateNormalDiag](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MultivariateNormalDiag) - [MultivariateNormalDiagPlusLowRank](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MultivariateNormalDiagPlusLowRank) - [MultivariateNormalDiagPlusLowRankCovariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MultivariateNormalDiagPlusLowRankCovariance) - [MultivariateNormalFullCovariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MultivariateNormalFullCovariance) - [MultivariateNormalLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MultivariateNormalLinearOperator) - [MultivariateNormalTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MultivariateNormalTriL) - [MultivariateStudentTLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MultivariateStudentTLinearOperator) - [NegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/NegativeBinomial) - [NoncentralChi2](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/NoncentralChi2) - [Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Normal) - [NormalInverseGaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/NormalInverseGaussian) - [OneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/OneHotCategorical) - [OrderedLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/OrderedLogistic) - [PERT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/PERT) - [Pareto](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Pareto) - [PlackettLuce](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/PlackettLuce) - [Poisson](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Poisson) - [PoissonLogNormalQuadratureCompound](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/PoissonLogNormalQuadratureCompound) - [PowerSpherical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/PowerSpherical) - [ProbitBernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/ProbitBernoulli) - [QuantizedDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/QuantizedDistribution) - [RegisterKL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/RegisterKL) - [RelaxedBernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/RelaxedBernoulli) - [RelaxedOneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/RelaxedOneHotCategorical) - [Sample](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Sample) - [SigmoidBeta](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/SigmoidBeta) - [SinhArcsinh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/SinhArcsinh) - [Skellam](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Skellam) - [SphericalUniform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/SphericalUniform) - [StoppingRatioLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/StoppingRatioLogistic) - [StudentT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/StudentT) - [StudentTProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/StudentTProcess) - [StudentTProcessRegressionModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/StudentTProcessRegressionModel) - [TransformedDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/TransformedDistribution) - [Triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Triangular) - [TruncatedCauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/TruncatedCauchy) - [TruncatedNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/TruncatedNormal) - [TwoPieceNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/TwoPieceNormal) - [TwoPieceStudentT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/TwoPieceStudentT) - [Uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Uniform) - [VariationalGaussianProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/VariationalGaussianProcess) - [VectorDeterministic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/VectorDeterministic) - [VonMises](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/VonMises) - [VonMisesFisher](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/VonMisesFisher) - [Weibull](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Weibull) - [WishartLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/WishartLinearOperator) - [WishartTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/WishartTriL) - [ZeroInflatedNegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/ZeroInflatedNegativeBinomial) - [Zipf](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Zipf) - [independent\_joint\_distribution\_from\_structure](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/independent_joint_distribution_from_structure) - [kl\_divergence](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/kl_divergence) - [mvn\_conjugate\_linear\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/mvn_conjugate_linear_update) - [normal\_conjugates\_known\_scale\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/normal_conjugates_known_scale_posterior) - [normal\_conjugates\_known\_scale\_predictive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/normal_conjugates_known_scale_predictive) - [quadrature\_scheme\_lognormal\_gauss\_hermite](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/quadrature_scheme_lognormal_gauss_hermite) - [quadrature\_scheme\_lognormal\_quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/quadrature_scheme_lognormal_quantiles) - glm - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm) - [Bernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/Bernoulli) - [BernoulliNormalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/BernoulliNormalCDF) - [Binomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/Binomial) - [CustomExponentialFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/CustomExponentialFamily) - [ExponentialFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/ExponentialFamily) - [GammaExp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/GammaExp) - [GammaSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/GammaSoftplus) - [LogNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/LogNormal) - [LogNormalSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/LogNormalSoftplus) - [NegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/NegativeBinomial) - [NegativeBinomialSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/NegativeBinomialSoftplus) - [Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/Normal) - [NormalReciprocal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/NormalReciprocal) - [Poisson](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/Poisson) - [PoissonSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/PoissonSoftplus) - [compute\_predicted\_linear\_response](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/compute_predicted_linear_response) - [convergence\_criteria\_small\_relative\_norm\_weights\_change](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/convergence_criteria_small_relative_norm_weights_change) - [fit](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/fit) - [fit\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/fit_one_step) - math - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math) - [MinimizeTraceableQuantities](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/MinimizeTraceableQuantities) - [atan\_difference](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/atan_difference) - [batch\_interp\_rectilinear\_nd\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/batch_interp_rectilinear_nd_grid) - [batch\_interp\_regular\_1d\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/batch_interp_regular_1d_grid) - [batch\_interp\_regular\_nd\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/batch_interp_regular_nd_grid) - [bessel\_iv\_ratio](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/bessel_iv_ratio) - [bessel\_ive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/bessel_ive) - [bessel\_kve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/bessel_kve) - [betainc](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/betainc) - [betaincinv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/betaincinv) - [bracket\_root](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/bracket_root) - [cholesky\_concat](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/cholesky_concat) - [cholesky\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/cholesky_update) - [clip\_by\_value\_preserve\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/clip_by_value_preserve_gradient) - [custom\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/custom_gradient) - [dawsn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/dawsn) - [diag\_jacobian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/diag_jacobian) - [erfcinv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/erfcinv) - [erfcx](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/erfcx) - [fill\_triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/fill_triangular) - [fill\_triangular\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/fill_triangular_inverse) - [find\_root\_chandrupatla](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/find_root_chandrupatla) - [find\_root\_secant](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/find_root_secant) - [gram\_schmidt](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/gram_schmidt) - [hpsd\_logdet](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/hpsd_logdet) - [hpsd\_quadratic\_form\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/hpsd_quadratic_form_solve) - [hpsd\_quadratic\_form\_solvevec](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/hpsd_quadratic_form_solvevec) - [hpsd\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/hpsd_solve) - [hpsd\_solvevec](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/hpsd_solvevec) - [igammacinv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/igammacinv) - [igammainv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/igammainv) - [interp\_regular\_1d\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/interp_regular_1d_grid) - [lambertw](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/lambertw) - [lambertw\_winitzki\_approx](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/lambertw_winitzki_approx) - [lbeta](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/lbeta) - [log1mexp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log1mexp) - [log1psquare](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log1psquare) - [log\_add\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_add_exp) - [log\_bessel\_ive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_bessel_ive) - [log\_bessel\_kve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_bessel_kve) - [log\_combinations](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_combinations) - [log\_cosh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_cosh) - [log\_cumsum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_cumsum_exp) - [log\_gamma\_correction](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_gamma_correction) - [log\_gamma\_difference](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_gamma_difference) - [log\_sub\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_sub_exp) - [logerfc](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/logerfc) - [logerfcx](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/logerfcx) - [low\_rank\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/low_rank_cholesky) - [lu\_matrix\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/lu_matrix_inverse) - [lu\_reconstruct](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/lu_reconstruct) - [lu\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/lu_solve) - [minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/minimize) - [minimize\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/minimize_stateless) - [owens\_t](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/owens_t) - [pivoted\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/pivoted_cholesky) - [reduce\_kahan\_sum](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/reduce_kahan_sum) - [reduce\_log\_harmonic\_mean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/reduce_log_harmonic_mean_exp) - [reduce\_logmeanexp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/reduce_logmeanexp) - [reduce\_weighted\_logsumexp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/reduce_weighted_logsumexp) - [round\_exponential\_bump\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/round_exponential_bump_function) - [scan\_associative](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/scan_associative) - [smootherstep](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/smootherstep) - [soft\_sorting\_matrix](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/soft_sorting_matrix) - [soft\_threshold](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/soft_threshold) - [softplus\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/softplus_inverse) - [sparse\_or\_dense\_matmul](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/sparse_or_dense_matmul) - [sparse\_or\_dense\_matvecmul](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/sparse_or_dense_matvecmul) - [sqrt1pm1](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/sqrt1pm1) - [trapz](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/trapz) - [value\_and\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/value_and_gradient) - hypergeometric - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/hypergeometric) - [hyp2f1\_small\_argument](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/hypergeometric/hyp2f1_small_argument) - ode - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/ode) - [BDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/ode/BDF) - [ChosenBySolver](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/ode/ChosenBySolver) - [Diagnostics](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/ode/Diagnostics) - [DormandPrince](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/ode/DormandPrince) - [Results](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/ode/Results) - [Solver](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/ode/Solver) - psd\_kernels - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels) - [AutoCompositeTensorPsdKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/AutoCompositeTensorPsdKernel) - [ChangePoint](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/ChangePoint) - [Constant](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/Constant) - [ExpSinSquared](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/ExpSinSquared) - [ExponentialCurve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/ExponentialCurve) - [ExponentiatedQuadratic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/ExponentiatedQuadratic) - [FeatureScaled](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/FeatureScaled) - [FeatureTransformed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/FeatureTransformed) - [GammaExponential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/GammaExponential) - [GeneralizedMatern](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/GeneralizedMatern) - [KumaraswamyTransformed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/KumaraswamyTransformed) - [Linear](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/Linear) - [MaternFiveHalves](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/MaternFiveHalves) - [MaternOneHalf](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/MaternOneHalf) - [MaternThreeHalves](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/MaternThreeHalves) - [Parabolic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/Parabolic) - [PointwiseExponential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/PointwiseExponential) - [Polynomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/Polynomial) - [PositiveSemidefiniteKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/PositiveSemidefiniteKernel) - [RationalQuadratic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/RationalQuadratic) - [SchurComplement](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/SchurComplement) - [SpectralMixture](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/SpectralMixture) - mcmc - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc) - [CheckpointableStatesAndTrace](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/CheckpointableStatesAndTrace) - [DualAveragingStepSizeAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/DualAveragingStepSizeAdaptation) - [HamiltonianMonteCarlo](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/HamiltonianMonteCarlo) - [MetropolisAdjustedLangevinAlgorithm](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/MetropolisAdjustedLangevinAlgorithm) - [MetropolisHastings](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/MetropolisHastings) - [NoUTurnSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/NoUTurnSampler) - [RandomWalkMetropolis](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/RandomWalkMetropolis) - [ReplicaExchangeMC](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/ReplicaExchangeMC) - [SimpleStepSizeAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/SimpleStepSizeAdaptation) - [SliceSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/SliceSampler) - [StatesAndTrace](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/StatesAndTrace) - [TransformedTransitionKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/TransformedTransitionKernel) - [TransitionKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/TransitionKernel) - [UncalibratedHamiltonianMonteCarlo](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/UncalibratedHamiltonianMonteCarlo) - [UncalibratedLangevin](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/UncalibratedLangevin) - [UncalibratedRandomWalk](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/UncalibratedRandomWalk) - [default\_swap\_proposal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/default_swap_proposal_fn) - [effective\_sample\_size](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/effective_sample_size) - [even\_odd\_swap\_proposal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/even_odd_swap_proposal_fn) - [make\_simple\_step\_size\_update\_policy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/make_simple_step_size_update_policy) - [potential\_scale\_reduction](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/potential_scale_reduction) - [random\_walk\_normal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/random_walk_normal_fn) - [random\_walk\_uniform\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/random_walk_uniform_fn) - [sample\_annealed\_importance\_chain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/sample_annealed_importance_chain) - [sample\_chain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/sample_chain) - [sample\_halton\_sequence](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/sample_halton_sequence) - monte\_carlo - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/monte_carlo) - [expectation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/monte_carlo/expectation) - optimizer - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer) - [bfgs\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/bfgs_minimize) - [converged\_all](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/converged_all) - [converged\_any](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/converged_any) - [lbfgs\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/lbfgs_minimize) - [nelder\_mead\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/nelder_mead_minimize) - [nelder\_mead\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/nelder_mead_one_step) - convergence\_criteria - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/convergence_criteria) - [ConvergenceCriterion](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/convergence_criteria/ConvergenceCriterion) - [LossNotDecreasing](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/convergence_criteria/LossNotDecreasing) - [SuccessiveGradientsAreUncorrelated](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/convergence_criteria/SuccessiveGradientsAreUncorrelated) - linesearch - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/linesearch) - [hager\_zhang](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/linesearch/hager_zhang) - random - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/random) - [rademacher](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/random/rademacher) - [rayleigh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/random/rayleigh) - [sanitize\_seed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/random/sanitize_seed) - [spherical\_uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/random/spherical_uniform) - [split\_seed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/random/split_seed) - stats - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats) - [assign\_log\_moving\_mean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/assign_log_moving_mean_exp) - [assign\_moving\_mean\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/assign_moving_mean_variance) - [auto\_correlation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/auto_correlation) - [brier\_decomposition](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/brier_decomposition) - [brier\_score](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/brier_score) - [cholesky\_covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/cholesky_covariance) - [correlation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/correlation) - [count\_integers](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/count_integers) - [covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/covariance) - [cumulative\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/cumulative_variance) - [expected\_calibration\_error](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/expected_calibration_error) - [expected\_calibration\_error\_quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/expected_calibration_error_quantiles) - [find\_bins](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/find_bins) - [histogram](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/histogram) - [kendalls\_tau](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/kendalls_tau) - [log\_average\_probs](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/log_average_probs) - [log\_loomean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/log_loomean_exp) - [log\_loosum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/log_loosum_exp) - [log\_soomean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/log_soomean_exp) - [log\_soosum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/log_soosum_exp) - [moving\_mean\_variance\_zero\_debiased](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/moving_mean_variance_zero_debiased) - [percentile](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/percentile) - [quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/quantiles) - [stddev](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/stddev) - [variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/variance) - [windowed\_mean](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/windowed_mean) - [windowed\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/windowed_variance) - sts - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts) - [AdditiveStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/AdditiveStateSpaceModel) - [Autoregressive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/Autoregressive) - [AutoregressiveIntegratedMovingAverage](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/AutoregressiveIntegratedMovingAverage) - [AutoregressiveMovingAverageStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/AutoregressiveMovingAverageStateSpaceModel) - [AutoregressiveStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/AutoregressiveStateSpaceModel) - [ConstrainedSeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/ConstrainedSeasonalStateSpaceModel) - [DynamicLinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/DynamicLinearRegression) - [DynamicLinearRegressionStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/DynamicLinearRegressionStateSpaceModel) - [IntegratedStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/IntegratedStateSpaceModel) - [LinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/LinearRegression) - [LocalLevel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/LocalLevel) - [LocalLevelStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/LocalLevelStateSpaceModel) - [LocalLinearTrend](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/LocalLinearTrend) - [LocalLinearTrendStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/LocalLinearTrendStateSpaceModel) - [MaskedTimeSeries](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/MaskedTimeSeries) - [MissingValuesTolerance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/MissingValuesTolerance) - [Seasonal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/Seasonal) - [SeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/SeasonalStateSpaceModel) - [SemiLocalLinearTrend](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/SemiLocalLinearTrend) - [SemiLocalLinearTrendStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/SemiLocalLinearTrendStateSpaceModel) - [SmoothSeasonal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/SmoothSeasonal) - [SmoothSeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/SmoothSeasonalStateSpaceModel) - [SparseLinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/SparseLinearRegression) - [StructuralTimeSeries](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/StructuralTimeSeries) - [Sum](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/Sum) - [build\_factored\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/build_factored_surrogate_posterior) - [build\_factored\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/build_factored_surrogate_posterior_stateless) - [decompose\_by\_component](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/decompose_by_component) - [decompose\_forecast\_by\_component](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/decompose_forecast_by_component) - [fit\_with\_hmc](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/fit_with_hmc) - [forecast](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/forecast) - [impute\_missing\_values](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/impute_missing_values) - [moments\_of\_masked\_time\_series](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/moments_of_masked_time_series) - [one\_step\_predictive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/one_step_predictive) - [regularize\_series](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/regularize_series) - [sample\_uniform\_initial\_state](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/sample_uniform_initial_state) - util - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/util) - [BatchedComponentProperties](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/util/BatchedComponentProperties) - [DeferredTensor](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/util/DeferredTensor) - [ParameterProperties](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/util/ParameterProperties) - [SeedStream](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/util/SeedStream) - [TransformedVariable](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/util/TransformedVariable) - vi - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi) - [GradientEstimators](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/GradientEstimators) - [amari\_alpha](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/amari_alpha) - [arithmetic\_geometric](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/arithmetic_geometric) - [chi\_square](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/chi_square) - [csiszar\_vimco](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/csiszar_vimco) - [dual\_csiszar\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/dual_csiszar_function) - [fit\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/fit_surrogate_posterior_stateless) - [jeffreys](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/jeffreys) - [jensen\_shannon](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/jensen_shannon) - [kl\_forward](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/kl_forward) - [kl\_reverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/kl_reverse) - [log1p\_abs](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/log1p_abs) - [modified\_gan](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/modified_gan) - [monte\_carlo\_variational\_loss](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/monte_carlo_variational_loss) - [pearson](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/pearson) - [squared\_hellinger](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/squared_hellinger) - [symmetrized\_csiszar\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/symmetrized_csiszar_function) - [t\_power](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/t_power) - [total\_variation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/total_variation) - [triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/triangular) - numpy - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy) - bijectors - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors) - [AbsoluteValue](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/AbsoluteValue) - [Ascending](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Ascending) - [AutoCompositeTensorBijector](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/AutoCompositeTensorBijector) - [AutoregressiveNetwork](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/AutoregressiveNetwork) - [Bijector](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Bijector) - [Blockwise](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Blockwise) - [Chain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Chain) - [CholeskyOuterProduct](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/CholeskyOuterProduct) - [CholeskyToInvCholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/CholeskyToInvCholesky) - [Composition](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Composition) - [CorrelationCholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/CorrelationCholesky) - [Cumsum](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Cumsum) - [Exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Exp) - [Expm1](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Expm1) - [FFJORD](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/FFJORD) - [FillScaleTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/FillScaleTriL) - [FillTriangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/FillTriangular) - [FrechetCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/FrechetCDF) - [GeneralizedExtremeValueCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/GeneralizedExtremeValueCDF) - [GeneralizedPareto](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/GeneralizedPareto) - [GompertzCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/GompertzCDF) - [GumbelCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/GumbelCDF) - [Householder](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Householder) - [Identity](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Identity) - [Inline](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Inline) - [Invert](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Invert) - [IteratedSigmoidCentered](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/IteratedSigmoidCentered) - [JointMap](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/JointMap) - [KumaraswamyCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/KumaraswamyCDF) - [LambertWTail](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/LambertWTail) - [Log](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Log) - [Log1p](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Log1p) - [MaskedAutoregressiveFlow](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/MaskedAutoregressiveFlow) - [MatrixInverseTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/MatrixInverseTriL) - [MatvecLU](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/MatvecLU) - [MoyalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/MoyalCDF) - [NormalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/NormalCDF) - [Pad](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Pad) - [Permute](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Permute) - [Power](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Power) - [PowerTransform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/PowerTransform) - [RationalQuadraticSpline](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/RationalQuadraticSpline) - [RayleighCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/RayleighCDF) - [RealNVP](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/RealNVP) - [Reciprocal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Reciprocal) - [Reshape](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Reshape) - [Restructure](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Restructure) - [Scale](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Scale) - [ScaleMatvecDiag](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/ScaleMatvecDiag) - [ScaleMatvecLU](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/ScaleMatvecLU) - [ScaleMatvecLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/ScaleMatvecLinearOperator) - [ScaleMatvecLinearOperatorBlock](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/ScaleMatvecLinearOperatorBlock) - [ScaleMatvecTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/ScaleMatvecTriL) - [Shift](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Shift) - [ShiftedGompertzCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/ShiftedGompertzCDF) - [Sigmoid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Sigmoid) - [Sinh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Sinh) - [SinhArcsinh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/SinhArcsinh) - [SoftClip](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/SoftClip) - [Softfloor](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Softfloor) - [SoftmaxCentered](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/SoftmaxCentered) - [Softplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Softplus) - [Softsign](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Softsign) - [Split](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Split) - [Square](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Square) - [Tanh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Tanh) - [TransformDiagonal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/TransformDiagonal) - [Transpose](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Transpose) - [UnitVector](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/UnitVector) - [WeibullCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/WeibullCDF) - [masked\_autoregressive\_default\_template](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/masked_autoregressive_default_template) - [masked\_dense](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/masked_dense) - [pack\_sequence\_as](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/pack_sequence_as) - [real\_nvp\_default\_template](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/real_nvp_default_template) - [tree\_flatten](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/tree_flatten) - distributions - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions) - [AutoCompositeTensorDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/AutoCompositeTensorDistribution) - [Autoregressive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Autoregressive) - [BatchBroadcast](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/BatchBroadcast) - [BatchReshape](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/BatchReshape) - [Bates](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Bates) - [Bernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Bernoulli) - [Beta](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Beta) - [BetaBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/BetaBinomial) - [BetaQuotient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/BetaQuotient) - [Binomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Binomial) - [Blockwise](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Blockwise) - [Categorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Categorical) - [Cauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Cauchy) - [Chi](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Chi) - [Chi2](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Chi2) - [CholeskyLKJ](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/CholeskyLKJ) - [DeterminantalPointProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/DeterminantalPointProcess) - [Deterministic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Deterministic) - [Dirichlet](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Dirichlet) - [DirichletMultinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/DirichletMultinomial) - [Distribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Distribution) - [DoublesidedMaxwell](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/DoublesidedMaxwell) - [Empirical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Empirical) - [ExpGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/ExpGamma) - [ExpInverseGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/ExpInverseGamma) - [ExpRelaxedOneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/ExpRelaxedOneHotCategorical) - [Exponential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Exponential) - [ExponentiallyModifiedGaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/ExponentiallyModifiedGaussian) - [FiniteDiscrete](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/FiniteDiscrete) - [Gamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Gamma) - [GammaGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/GammaGamma) - [GaussianProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/GaussianProcess) - [GaussianProcessRegressionModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/GaussianProcessRegressionModel) - [GeneralizedExtremeValue](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/GeneralizedExtremeValue) - [GeneralizedNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/GeneralizedNormal) - [GeneralizedPareto](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/GeneralizedPareto) - [Geometric](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Geometric) - [Gumbel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Gumbel) - [HalfCauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/HalfCauchy) - [HalfNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/HalfNormal) - [HalfStudentT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/HalfStudentT) - [HiddenMarkovModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/HiddenMarkovModel) - [Horseshoe](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Horseshoe) - [Independent](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Independent) - [Inflated](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Inflated) - [InverseGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/InverseGamma) - [InverseGaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/InverseGaussian) - [JohnsonSU](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JohnsonSU) - [JointDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistribution) - [JointDistribution.Root](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistribution/Root) - [JointDistributionCoroutine](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistributionCoroutine) - [JointDistributionCoroutineAutoBatched](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistributionCoroutineAutoBatched) - [JointDistributionNamed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistributionNamed) - [JointDistributionNamedAutoBatched](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistributionNamedAutoBatched) - [JointDistributionSequential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistributionSequential) - [JointDistributionSequentialAutoBatched](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistributionSequentialAutoBatched) - [Kumaraswamy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Kumaraswamy) - [LKJ](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/LKJ) - [LambertWDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/LambertWDistribution) - [LambertWNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/LambertWNormal) - [Laplace](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Laplace) - [LinearGaussianStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/LinearGaussianStateSpaceModel) - [LogLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/LogLogistic) - [LogNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/LogNormal) - [Logistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Logistic) - [LogitNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/LogitNormal) - [MarkovChain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MarkovChain) - [Masked](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Masked) - [MatrixNormalLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MatrixNormalLinearOperator) - [MatrixTLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MatrixTLinearOperator) - [Mixture](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Mixture) - [MixtureSameFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MixtureSameFamily) - [Moyal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Moyal) - [Multinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Multinomial) - [MultivariateNormalDiag](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MultivariateNormalDiag) - [MultivariateNormalDiagPlusLowRank](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MultivariateNormalDiagPlusLowRank) - [MultivariateNormalDiagPlusLowRankCovariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MultivariateNormalDiagPlusLowRankCovariance) - [MultivariateNormalFullCovariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MultivariateNormalFullCovariance) - [MultivariateNormalLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MultivariateNormalLinearOperator) - [MultivariateNormalTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MultivariateNormalTriL) - [MultivariateStudentTLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MultivariateStudentTLinearOperator) - [NegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/NegativeBinomial) - [NoncentralChi2](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/NoncentralChi2) - [Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Normal) - [NormalInverseGaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/NormalInverseGaussian) - [OneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/OneHotCategorical) - [OrderedLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/OrderedLogistic) - [PERT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/PERT) - [Pareto](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Pareto) - [PlackettLuce](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/PlackettLuce) - [Poisson](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Poisson) - [PoissonLogNormalQuadratureCompound](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/PoissonLogNormalQuadratureCompound) - [PowerSpherical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/PowerSpherical) - [ProbitBernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/ProbitBernoulli) - [QuantizedDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/QuantizedDistribution) - [RegisterKL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/RegisterKL) - [RelaxedBernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/RelaxedBernoulli) - [RelaxedOneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/RelaxedOneHotCategorical) - [Sample](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Sample) - [SigmoidBeta](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/SigmoidBeta) - [SinhArcsinh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/SinhArcsinh) - [Skellam](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Skellam) - [SphericalUniform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/SphericalUniform) - [StoppingRatioLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/StoppingRatioLogistic) - [StudentT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/StudentT) - [StudentTProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/StudentTProcess) - [StudentTProcessRegressionModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/StudentTProcessRegressionModel) - [TransformedDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/TransformedDistribution) - [Triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Triangular) - [TruncatedCauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/TruncatedCauchy) - [TruncatedNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/TruncatedNormal) - [TwoPieceNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/TwoPieceNormal) - [TwoPieceStudentT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/TwoPieceStudentT) - [Uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Uniform) - [VariationalGaussianProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/VariationalGaussianProcess) - [VectorDeterministic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/VectorDeterministic) - [VonMises](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/VonMises) - [VonMisesFisher](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/VonMisesFisher) - [Weibull](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Weibull) - [WishartLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/WishartLinearOperator) - [WishartTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/WishartTriL) - [ZeroInflatedNegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/ZeroInflatedNegativeBinomial) - [Zipf](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Zipf) - [independent\_joint\_distribution\_from\_structure](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/independent_joint_distribution_from_structure) - [kl\_divergence](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/kl_divergence) - [mvn\_conjugate\_linear\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/mvn_conjugate_linear_update) - [normal\_conjugates\_known\_scale\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/normal_conjugates_known_scale_posterior) - [normal\_conjugates\_known\_scale\_predictive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/normal_conjugates_known_scale_predictive) - [quadrature\_scheme\_lognormal\_gauss\_hermite](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/quadrature_scheme_lognormal_gauss_hermite) - [quadrature\_scheme\_lognormal\_quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/quadrature_scheme_lognormal_quantiles) - glm - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm) - [Bernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/Bernoulli) - [BernoulliNormalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/BernoulliNormalCDF) - [Binomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/Binomial) - [CustomExponentialFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/CustomExponentialFamily) - [ExponentialFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/ExponentialFamily) - [GammaExp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/GammaExp) - [GammaSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/GammaSoftplus) - [LogNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/LogNormal) - [LogNormalSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/LogNormalSoftplus) - [NegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/NegativeBinomial) - [NegativeBinomialSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/NegativeBinomialSoftplus) - [Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/Normal) - [NormalReciprocal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/NormalReciprocal) - [Poisson](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/Poisson) - [PoissonSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/PoissonSoftplus) - [compute\_predicted\_linear\_response](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/compute_predicted_linear_response) - [convergence\_criteria\_small\_relative\_norm\_weights\_change](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/convergence_criteria_small_relative_norm_weights_change) - [fit](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/fit) - [fit\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/fit_one_step) - math - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math) - [MinimizeTraceableQuantities](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/MinimizeTraceableQuantities) - [atan\_difference](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/atan_difference) - [batch\_interp\_rectilinear\_nd\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/batch_interp_rectilinear_nd_grid) - [batch\_interp\_regular\_1d\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/batch_interp_regular_1d_grid) - [batch\_interp\_regular\_nd\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/batch_interp_regular_nd_grid) - [bessel\_iv\_ratio](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/bessel_iv_ratio) - [bessel\_ive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/bessel_ive) - [bessel\_kve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/bessel_kve) - [betainc](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/betainc) - [betaincinv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/betaincinv) - [bracket\_root](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/bracket_root) - [cholesky\_concat](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/cholesky_concat) - [cholesky\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/cholesky_update) - [clip\_by\_value\_preserve\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/clip_by_value_preserve_gradient) - [custom\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/custom_gradient) - [dawsn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/dawsn) - [diag\_jacobian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/diag_jacobian) - [erfcinv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/erfcinv) - [erfcx](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/erfcx) - [fill\_triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/fill_triangular) - [fill\_triangular\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/fill_triangular_inverse) - [find\_root\_chandrupatla](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/find_root_chandrupatla) - [find\_root\_secant](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/find_root_secant) - [gram\_schmidt](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/gram_schmidt) - [hpsd\_logdet](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/hpsd_logdet) - [hpsd\_quadratic\_form\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/hpsd_quadratic_form_solve) - [hpsd\_quadratic\_form\_solvevec](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/hpsd_quadratic_form_solvevec) - [hpsd\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/hpsd_solve) - [hpsd\_solvevec](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/hpsd_solvevec) - [igammacinv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/igammacinv) - [igammainv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/igammainv) - [interp\_regular\_1d\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/interp_regular_1d_grid) - [lambertw](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/lambertw) - [lambertw\_winitzki\_approx](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/lambertw_winitzki_approx) - [lbeta](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/lbeta) - [log1mexp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log1mexp) - [log1psquare](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log1psquare) - [log\_add\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_add_exp) - [log\_bessel\_ive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_bessel_ive) - [log\_bessel\_kve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_bessel_kve) - [log\_combinations](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_combinations) - [log\_cosh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_cosh) - [log\_cumsum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_cumsum_exp) - [log\_gamma\_correction](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_gamma_correction) - [log\_gamma\_difference](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_gamma_difference) - [log\_sub\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_sub_exp) - [logerfc](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/logerfc) - [logerfcx](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/logerfcx) - [low\_rank\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/low_rank_cholesky) - [lu\_matrix\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/lu_matrix_inverse) - [lu\_reconstruct](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/lu_reconstruct) - [lu\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/lu_solve) - [minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/minimize) - [minimize\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/minimize_stateless) - [owens\_t](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/owens_t) - [pivoted\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/pivoted_cholesky) - [reduce\_kahan\_sum](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/reduce_kahan_sum) - [reduce\_log\_harmonic\_mean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/reduce_log_harmonic_mean_exp) - [reduce\_logmeanexp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/reduce_logmeanexp) - [reduce\_weighted\_logsumexp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/reduce_weighted_logsumexp) - [round\_exponential\_bump\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/round_exponential_bump_function) - [scan\_associative](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/scan_associative) - [smootherstep](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/smootherstep) - [soft\_sorting\_matrix](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/soft_sorting_matrix) - [soft\_threshold](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/soft_threshold) - [softplus\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/softplus_inverse) - [sparse\_or\_dense\_matmul](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/sparse_or_dense_matmul) - [sparse\_or\_dense\_matvecmul](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/sparse_or_dense_matvecmul) - [sqrt1pm1](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/sqrt1pm1) - [trapz](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/trapz) - [value\_and\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/value_and_gradient) - hypergeometric - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/hypergeometric) - [hyp2f1\_small\_argument](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/hypergeometric/hyp2f1_small_argument) - ode - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/ode) - [BDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/ode/BDF) - [ChosenBySolver](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/ode/ChosenBySolver) - [Diagnostics](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/ode/Diagnostics) - [DormandPrince](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/ode/DormandPrince) - [Results](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/ode/Results) - [Solver](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/ode/Solver) - psd\_kernels - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels) - [AutoCompositeTensorPsdKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/AutoCompositeTensorPsdKernel) - [ChangePoint](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/ChangePoint) - [Constant](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/Constant) - [ExpSinSquared](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/ExpSinSquared) - [ExponentialCurve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/ExponentialCurve) - [ExponentiatedQuadratic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/ExponentiatedQuadratic) - [FeatureScaled](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/FeatureScaled) - [FeatureTransformed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/FeatureTransformed) - [GammaExponential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/GammaExponential) - [GeneralizedMatern](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/GeneralizedMatern) - [KumaraswamyTransformed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/KumaraswamyTransformed) - [Linear](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/Linear) - [MaternFiveHalves](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/MaternFiveHalves) - [MaternOneHalf](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/MaternOneHalf) - [MaternThreeHalves](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/MaternThreeHalves) - [Parabolic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/Parabolic) - [PointwiseExponential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/PointwiseExponential) - [Polynomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/Polynomial) - [PositiveSemidefiniteKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/PositiveSemidefiniteKernel) - [RationalQuadratic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/RationalQuadratic) - [SchurComplement](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/SchurComplement) - [SpectralMixture](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/SpectralMixture) - mcmc - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc) - [CheckpointableStatesAndTrace](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/CheckpointableStatesAndTrace) - [DualAveragingStepSizeAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/DualAveragingStepSizeAdaptation) - [MetropolisHastings](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/MetropolisHastings) - [RandomWalkMetropolis](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/RandomWalkMetropolis) - [ReplicaExchangeMC](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/ReplicaExchangeMC) - [SimpleStepSizeAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/SimpleStepSizeAdaptation) - [SliceSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/SliceSampler) - [StatesAndTrace](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/StatesAndTrace) - [TransformedTransitionKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/TransformedTransitionKernel) - [TransitionKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/TransitionKernel) - [UncalibratedRandomWalk](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/UncalibratedRandomWalk) - [default\_swap\_proposal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/default_swap_proposal_fn) - [effective\_sample\_size](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/effective_sample_size) - [even\_odd\_swap\_proposal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/even_odd_swap_proposal_fn) - [potential\_scale\_reduction](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/potential_scale_reduction) - [random\_walk\_normal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/random_walk_normal_fn) - [random\_walk\_uniform\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/random_walk_uniform_fn) - [sample\_annealed\_importance\_chain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/sample_annealed_importance_chain) - [sample\_chain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/sample_chain) - [sample\_halton\_sequence](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/sample_halton_sequence) - monte\_carlo - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/monte_carlo) - [expectation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/monte_carlo/expectation) - optimizer - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer) - [bfgs\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/bfgs_minimize) - [converged\_all](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/converged_all) - [converged\_any](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/converged_any) - [lbfgs\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/lbfgs_minimize) - [nelder\_mead\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/nelder_mead_minimize) - [nelder\_mead\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/nelder_mead_one_step) - convergence\_criteria - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/convergence_criteria) - [ConvergenceCriterion](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/convergence_criteria/ConvergenceCriterion) - [LossNotDecreasing](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/convergence_criteria/LossNotDecreasing) - [SuccessiveGradientsAreUncorrelated](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/convergence_criteria/SuccessiveGradientsAreUncorrelated) - linesearch - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/linesearch) - [hager\_zhang](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/linesearch/hager_zhang) - random - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/random) - [rademacher](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/random/rademacher) - [rayleigh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/random/rayleigh) - [sanitize\_seed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/random/sanitize_seed) - [spherical\_uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/random/spherical_uniform) - [split\_seed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/random/split_seed) - stats - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats) - [assign\_log\_moving\_mean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/assign_log_moving_mean_exp) - [assign\_moving\_mean\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/assign_moving_mean_variance) - [auto\_correlation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/auto_correlation) - [brier\_decomposition](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/brier_decomposition) - [brier\_score](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/brier_score) - [cholesky\_covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/cholesky_covariance) - [correlation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/correlation) - [count\_integers](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/count_integers) - [covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/covariance) - [cumulative\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/cumulative_variance) - [expected\_calibration\_error](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/expected_calibration_error) - [expected\_calibration\_error\_quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/expected_calibration_error_quantiles) - [find\_bins](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/find_bins) - [histogram](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/histogram) - [kendalls\_tau](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/kendalls_tau) - [log\_average\_probs](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/log_average_probs) - [log\_loomean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/log_loomean_exp) - [log\_loosum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/log_loosum_exp) - [log\_soomean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/log_soomean_exp) - [log\_soosum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/log_soosum_exp) - [moving\_mean\_variance\_zero\_debiased](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/moving_mean_variance_zero_debiased) - [percentile](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/percentile) - [quantile\_auc](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/quantile_auc) - [quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/quantiles) - [stddev](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/stddev) - [variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/variance) - [windowed\_mean](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/windowed_mean) - [windowed\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/windowed_variance) - sts - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts) - [AdditiveStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/AdditiveStateSpaceModel) - [Autoregressive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/Autoregressive) - [AutoregressiveIntegratedMovingAverage](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/AutoregressiveIntegratedMovingAverage) - [AutoregressiveMovingAverageStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/AutoregressiveMovingAverageStateSpaceModel) - [AutoregressiveStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/AutoregressiveStateSpaceModel) - [ConstrainedSeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/ConstrainedSeasonalStateSpaceModel) - [DynamicLinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/DynamicLinearRegression) - [DynamicLinearRegressionStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/DynamicLinearRegressionStateSpaceModel) - [IntegratedStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/IntegratedStateSpaceModel) - [LinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/LinearRegression) - [LocalLevel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/LocalLevel) - [LocalLevelStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/LocalLevelStateSpaceModel) - [LocalLinearTrend](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/LocalLinearTrend) - [LocalLinearTrendStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/LocalLinearTrendStateSpaceModel) - [MaskedTimeSeries](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/MaskedTimeSeries) - [MissingValuesTolerance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/MissingValuesTolerance) - [Seasonal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/Seasonal) - [SeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/SeasonalStateSpaceModel) - [SemiLocalLinearTrend](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/SemiLocalLinearTrend) - [SemiLocalLinearTrendStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/SemiLocalLinearTrendStateSpaceModel) - [SmoothSeasonal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/SmoothSeasonal) - [SmoothSeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/SmoothSeasonalStateSpaceModel) - [SparseLinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/SparseLinearRegression) - [StructuralTimeSeries](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/StructuralTimeSeries) - [Sum](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/Sum) - [build\_factored\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/build_factored_surrogate_posterior) - [build\_factored\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/build_factored_surrogate_posterior_stateless) - [decompose\_by\_component](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/decompose_by_component) - [decompose\_forecast\_by\_component](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/decompose_forecast_by_component) - [fit\_with\_hmc](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/fit_with_hmc) - [forecast](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/forecast) - [impute\_missing\_values](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/impute_missing_values) - [moments\_of\_masked\_time\_series](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/moments_of_masked_time_series) - [one\_step\_predictive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/one_step_predictive) - [regularize\_series](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/regularize_series) - [sample\_uniform\_initial\_state](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/sample_uniform_initial_state) - util - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/util) - [BatchedComponentProperties](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/util/BatchedComponentProperties) - [DeferredTensor](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/util/DeferredTensor) - [ParameterProperties](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/util/ParameterProperties) - [SeedStream](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/util/SeedStream) - [TransformedVariable](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/util/TransformedVariable) - vi - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi) - [GradientEstimators](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/GradientEstimators) - [amari\_alpha](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/amari_alpha) - [arithmetic\_geometric](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/arithmetic_geometric) - [chi\_square](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/chi_square) - [csiszar\_vimco](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/csiszar_vimco) - [dual\_csiszar\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/dual_csiszar_function) - [fit\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/fit_surrogate_posterior) - [fit\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/fit_surrogate_posterior_stateless) - [jeffreys](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/jeffreys) - [jensen\_shannon](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/jensen_shannon) - [kl\_forward](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/kl_forward) - [kl\_reverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/kl_reverse) - [log1p\_abs](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/log1p_abs) - [modified\_gan](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/modified_gan) - [monte\_carlo\_variational\_loss](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/monte_carlo_variational_loss) - [pearson](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/pearson) - [squared\_hellinger](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/squared_hellinger) - [symmetrized\_csiszar\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/symmetrized_csiszar_function) - [t\_power](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/t_power) - [total\_variation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/total_variation) - [triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/triangular) - tfp. util - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/util) - [BatchedComponentProperties](https://www.tensorflow.org/probability/api_docs/python/tfp/util/BatchedComponentProperties) - [DeferredTensor](https://www.tensorflow.org/probability/api_docs/python/tfp/util/DeferredTensor) - [ParameterProperties](https://www.tensorflow.org/probability/api_docs/python/tfp/util/ParameterProperties) - [SeedStream](https://www.tensorflow.org/probability/api_docs/python/tfp/util/SeedStream) - [TransformedVariable](https://www.tensorflow.org/probability/api_docs/python/tfp/util/TransformedVariable) - tfp. vi - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/vi) - [GradientEstimators](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/GradientEstimators) - [amari\_alpha](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/amari_alpha) - [arithmetic\_geometric](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/arithmetic_geometric) - [chi\_square](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/chi_square) - [csiszar\_vimco](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/csiszar_vimco) - [dual\_csiszar\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/dual_csiszar_function) - [fit\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/fit_surrogate_posterior) - [fit\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/fit_surrogate_posterior_stateless) - [jeffreys](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/jeffreys) - [jensen\_shannon](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/jensen_shannon) - [kl\_forward](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/kl_forward) - [kl\_reverse](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/kl_reverse) - [log1p\_abs](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/log1p_abs) - [modified\_gan](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/modified_gan) - [monte\_carlo\_variational\_loss](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/monte_carlo_variational_loss) - [pearson](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/pearson) - [squared\_hellinger](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/squared_hellinger) - [symmetrized\_csiszar\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/symmetrized_csiszar_function) - [t\_power](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/t_power) - [total\_variation](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/total_variation) - [triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/triangular) - mutual\_information - [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/mutual_information) - [lower\_bound\_barber\_agakov](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/mutual_information/lower_bound_barber_agakov) - [lower\_bound\_info\_nce](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/mutual_information/lower_bound_info_nce) - [lower\_bound\_jensen\_shannon](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/mutual_information/lower_bound_jensen_shannon) - [lower\_bound\_nguyen\_wainwright\_jordan](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/mutual_information/lower_bound_nguyen_wainwright_jordan) - [Introduction](https://www.tensorflow.org/learn) - [Tutorials](https://www.tensorflow.org/tutorials) - [Guide](https://www.tensorflow.org/guide) - [Learn ML](https://www.tensorflow.org/resources/learn-ml) - [TensorFlow (v2.16.1)](https://www.tensorflow.org/api/stable) - [Versions…](https://www.tensorflow.org/versions) - [TensorFlow.js](https://js.tensorflow.org/api/latest/) - [TensorFlow Lite](https://www.tensorflow.org/lite/api_docs) - [TFX](https://www.tensorflow.org/tfx/api_docs) - LIBRARIES - [TensorFlow.js](https://www.tensorflow.org/js) - [TensorFlow Lite](https://www.tensorflow.org/lite) - [TFX](https://www.tensorflow.org/tfx) - [All libraries](https://www.tensorflow.org/resources/libraries-extensions) - 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[cdf](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#cdf) - [copy](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#copy) - [covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#covariance) - [cross\_entropy](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#cross_entropy) - [entropy](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#entropy) - [event\_shape\_tensor](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#event_shape_tensor) - [experimental\_default\_event\_space\_bijector](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#experimental_default_event_space_bijector) - [experimental\_fit](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#experimental_fit) - [experimental\_from\_mean\_concentration](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#experimental_from_mean_concentration) - [experimental\_from\_mean\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#experimental_from_mean_variance) - [experimental\_local\_measure](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#experimental_local_measure) - [experimental\_sample\_and\_log\_prob](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#experimental_sample_and_log_prob) - [is\_scalar\_batch](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#is_scalar_batch) - [is\_scalar\_event](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#is_scalar_event) - [kl\_divergence](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#kl_divergence) - [log\_cdf](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#log_cdf) - [log\_prob](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#log_prob) - [log\_survival\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#log_survival_function) - [mean](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#mean) - [mode](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#mode) - [param\_shapes](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#param_shapes) - [param\_static\_shapes](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#param_static_shapes) - [parameter\_properties](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#parameter_properties) - [prob](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#prob) - [quantile](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#quantile) - [sample](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#sample) - [stddev](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#stddev) - [survival\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#survival_function) - [unnormalized\_log\_prob](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#unnormalized_log_prob) - [variance](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#variance) - [with\_name\_scope](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#with_name_scope) - [\_\_getitem\_\_](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#__getitem__) - [\_\_iter\_\_](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#__iter__) - [TensorFlow](https://www.tensorflow.org/) - [Resources](https://www.tensorflow.org/resources) - [Probability](https://www.tensorflow.org/probability) - [API](https://www.tensorflow.org/probability/api_docs/python/tfp) Was this helpful? # tfp.distributions.BetaStay organized with collections Save and categorize content based on your preferences. - On this page - [Args](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#args) - [Attributes](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#attributes) - [Methods](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#methods) - [batch\_shape\_tensor](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#batch_shape_tensor) - [cdf](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#cdf) - [copy](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#copy) - [covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#covariance) - [cross\_entropy](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#cross_entropy) - [entropy](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#entropy) - [event\_shape\_tensor](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#event_shape_tensor) - [experimental\_default\_event\_space\_bijector](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#experimental_default_event_space_bijector) - [experimental\_fit](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#experimental_fit) - [experimental\_from\_mean\_concentration](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#experimental_from_mean_concentration) - [experimental\_from\_mean\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#experimental_from_mean_variance) - [experimental\_local\_measure](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#experimental_local_measure) - [experimental\_sample\_and\_log\_prob](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#experimental_sample_and_log_prob) - [is\_scalar\_batch](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#is_scalar_batch) - [is\_scalar\_event](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#is_scalar_event) - [kl\_divergence](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#kl_divergence) - [log\_cdf](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#log_cdf) - [log\_prob](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#log_prob) - [log\_survival\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#log_survival_function) - [mean](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#mean) - [mode](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#mode) - [param\_shapes](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#param_shapes) - [param\_static\_shapes](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#param_static_shapes) - [parameter\_properties](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#parameter_properties) - [prob](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#prob) - [quantile](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#quantile) - [sample](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#sample) - [stddev](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#stddev) - [survival\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#survival_function) - [unnormalized\_log\_prob](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#unnormalized_log_prob) - [variance](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#variance) - [with\_name\_scope](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#with_name_scope) - [\_\_getitem\_\_](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#__getitem__) - [\_\_iter\_\_](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta#__iter__) | | |---| | [![](https://www.tensorflow.org/images/GitHub-Mark-32px.png) View source on GitHub](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/beta.py#L45-L416) | Beta distribution. Inherits From: [`AutoCompositeTensorDistribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/AutoCompositeTensorDistribution), [`Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution), [`AutoCompositeTensor`](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/AutoCompositeTensor) ``` tfp.distributions.Beta( concentration1, concentration0, validate_args=False, allow_nan_stats=True, force_probs_to_zero_outside_support=False, name='Beta' ) ``` The Beta distribution is defined over the `(0, 1)` interval using parameters `concentration1` (aka 'alpha') and `concentration0` (aka 'beta'). #### Mathematical Details The probability density function (pdf) is, ``` pdf(x; alpha, beta) = x**(alpha - 1) (1 - x)**(beta - 1) / Z Z = Gamma(alpha) Gamma(beta) / Gamma(alpha + beta) ``` where: - `concentration1 = alpha`, - `concentration0 = beta`, - `Z` is the normalization constant, and, - `Gamma` is the [gamma function](https://en.wikipedia.org/wiki/Gamma_function). The concentration parameters represent mean total counts of a `1` or a `0`, i.e., ``` concentration1 = alpha = mean * total_concentration concentration0 = beta = (1. - mean) * total_concentration ``` where `mean` in `(0, 1)` and `total_concentration` is a positive real number representing a mean `total_count = concentration1 + concentration0`. Distribution parameters are automatically broadcast in all functions; see examples for details. **Warning:** The samples can be zero due to finite precision. This happens more often when some of the concentrations are very small. Make sure to round the samples to `np.finfo(dtype).tiny` before computing the density. Samples of this distribution are reparameterized (pathwise differentiable). The derivatives are computed using the approach described in the paper [Michael Figurnov, Shakir Mohamed, Andriy Mnih. Implicit Reparameterization Gradients, 2018](https://arxiv.org/abs/1805.08498) #### Examples ``` import tensorflow_probability as tfp tfd = tfp.distributions # Create a batch of three Beta distributions. alpha = [1, 2, 3] beta = [1, 2, 3] dist = tfd.Beta(alpha, beta) dist.sample([4, 5]) # Shape [4, 5, 3] # `x` has three batch entries, each with two samples. x = [[.1, .4, .5], [.2, .3, .5]] # Calculate the probability of each pair of samples under the corresponding # distribution in `dist`. dist.prob(x) # Shape [2, 3] # Define an equivalent Beta distribution parameterized by `mean` and # `total_concentration`: dist = tfd.Beta.experimental_from_mean_concentration( mean=0.5, total_concentration=alpha+beta) ``` ``` # Create batch_shape=[2, 3] via parameter broadcast: alpha = [[1.], [2]] # Shape [2, 1] beta = [3., 4, 5] # Shape [3] dist = tfd.Beta(alpha, beta) # alpha broadcast as: [[1., 1, 1,], # [2, 2, 2]] # beta broadcast as: [[3., 4, 5], # [3, 4, 5]] # batch_Shape [2, 3] dist.sample([4, 5]) # Shape [4, 5, 2, 3] x = [.2, .3, .5] # x will be broadcast as [[.2, .3, .5], # [.2, .3, .5]], # thus matching batch_shape [2, 3]. dist.prob(x) # Shape [2, 3] ``` Compute the gradients of samples w.r.t. the parameters: ``` alpha = tf.constant(1.0) beta = tf.constant(2.0) dist = tfd.Beta(alpha, beta) samples = dist.sample(5) # Shape [5] loss = tf.reduce_mean(tf.square(samples)) # Arbitrary loss function # Unbiased stochastic gradients of the loss function grads = tf.gradients(loss, [alpha, beta]) ``` | Args | | |---|---| | `concentration1` | Positive floating-point `Tensor` indicating mean number of successes; aka 'alpha'. | | `concentration0` | Positive floating-point `Tensor` indicating mean number of failures; aka 'beta'. | | `validate_args` | Python `bool`, default `False`. When `True` distribution parameters are checked for validity despite possibly degrading runtime performance. When `False` invalid inputs may silently render incorrect outputs. | | `allow_nan_stats` | Python `bool`, default `True`. When `True`, statistics (e.g., mean, mode, variance) use the value '`NaN`' to indicate the result is undefined. When `False`, an exception is raised if one or more of the statistic's batch members are undefined. | | `force_probs_to_zero_outside_support` | If `True`, force `prob(x) == 0` and `log_prob(x) == -inf` for values of x outside the distribution support. | | `name` | Python `str` name prefixed to Ops created by this class. | | Attributes | | |---|---| | `allow_nan_stats` | Python `bool` describing behavior when a stat is undefined. Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E\[(X - mean)\*\*2\] is also undefined. | | `batch_shape` | Shape of a single sample from a single event index as a `TensorShape`. May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution. | | `concentration0` | Concentration parameter associated with a `0` outcome. | | `concentration1` | Concentration parameter associated with a `1` outcome. | | `dtype` | The `DType` of `Tensor`s handled by this `Distribution`. | | `event_shape` | Shape of a single sample from a single batch as a `TensorShape`. May be partially defined or unknown. | | `experimental_shard_axis_names` | The list or structure of lists of active shard axis names. | | `force_probs_to_zero_outside_support` | | | `name` | Name prepended to all ops created by this `Distribution`. | | `name_scope` | Returns a [`tf.name_scope`](https://www.tensorflow.org/api_docs/python/tf/name_scope) instance for this class. | | `non_trainable_variables` | Sequence of non-trainable variables owned by this module and its submodules. **Note:** this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change. | | `parameters` | Dictionary of parameters used to instantiate this `Distribution`. | | `reparameterization_type` | Describes how samples from the distribution are reparameterized. Currently this is one of the static instances `tfd.FULLY_REPARAMETERIZED` or `tfd.NOT_REPARAMETERIZED`. | | `submodules` | Sequence of all sub-modules. Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on). | | `trainable_variables` | Sequence of trainable variables owned by this module and its submodules. **Note:** this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change. | | `validate_args` | Python `bool` indicating possibly expensive checks are enabled. | | `variables` | Sequence of variables owned by this module and its submodules.**Note:** this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change. | ## Methods ### `batch_shape_tensor` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L992-L1030) ``` batch_shape_tensor( name='batch_shape_tensor' ) ``` Shape of a single sample from a single event index as a 1-D `Tensor`. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution. | Args | | |---|---| | `name` | name to give to the op | | Returns | | |---|---| | `batch_shape` | `Tensor`. | ### `cdf` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1411-L1429) ``` cdf( value, name='cdf', **kwargs ) ``` Cumulative distribution function. Given random variable `X`, the cumulative distribution function `cdf` is: ``` cdf(x) := P[X <= x] ``` Additional documentation from `Beta`: **Note:** `x` must have dtype `self.dtype` and be in `[0, 1].` It must have a shape compatible with `self.batch_shape()`. | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `cdf` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `copy` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L896-L924) ``` copy( **override_parameters_kwargs ) ``` Creates a deep copy of the distribution. **Note:** the copy distribution may continue to depend on the original initialization arguments. | Args | | |---|---| | `**override_parameters_kwargs` | String/value dictionary of initialization arguments to override with new values. | | Returns | | |---|---| | `distribution` | A new instance of `type(self)` initialized from the union of self.parameters and override\_parameters\_kwargs, i.e., `dict(self.parameters, **override_parameters_kwargs)`. | ### `covariance` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1648-L1686) ``` covariance( name='covariance', **kwargs ) ``` Covariance. Covariance is (possibly) defined only for non-scalar-event distributions. For example, for a length-`k`, vector-valued distribution, it is calculated as, ``` Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])] ``` where `Cov` is a (batch of) `k x k` matrix, `0 <= (i, j) < k`, and `E` denotes expectation. Alternatively, for non-vector, multivariate distributions (e.g., matrix-valued, Wishart), `Covariance` shall return a (batch of) matrices under some vectorization of the events, i.e., ``` Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above] ``` where `Cov` is a (batch of) `k' x k'` matrices, `0 <= (i, j) < k' = reduce_prod(event_shape)`, and `Vec` is some function mapping indices of this distribution's event dimensions to indices of a length-`k'` vector. | Args | | |---|---| | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `covariance` | Floating-point `Tensor` with shape `[B1, ..., Bn, k', k']` where the first `n` dimensions are batch coordinates and `k' = reduce_prod(self.event_shape)`. | ### `cross_entropy` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1701-L1724) ``` cross_entropy( other, name='cross_entropy' ) ``` Computes the (Shannon) cross entropy. Denote this distribution (`self`) by `P` and the `other` distribution by `Q`. Assuming `P, Q` are absolutely continuous with respect to one another and permit densities `p(x) dr(x)` and `q(x) dr(x)`, (Shannon) cross entropy is defined as: ``` H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x) ``` where `F` denotes the support of the random variable `X ~ P`. `other` types with built-in registrations: `Beta` | Args | | |---|---| | `other` | [`tfp.distributions.Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution) instance. | | `name` | Python `str` prepended to names of ops created by this function. | | Returns | | |---|---| | `cross_entropy` | `self.dtype` `Tensor` with shape `[B1, ..., Bn]` representing `n` different calculations of (Shannon) cross entropy. | ### `entropy` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1524-L1527) ``` entropy( name='entropy', **kwargs ) ``` Shannon entropy in nats. ### `event_shape_tensor` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1099-L1125) ``` event_shape_tensor( name='event_shape_tensor' ) ``` Shape of a single sample from a single batch as a 1-D int32 `Tensor`. | Args | | |---|---| | `name` | name to give to the op | | Returns | | |---|---| | `event_shape` | `Tensor`. | ### `experimental_default_event_space_bijector` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1768-L1797) ``` experimental_default_event_space_bijector( *args, **kwargs ) ``` Bijector mapping the reals (R\*\*n) to the event space of the distribution. Distributions with continuous support may implement `_default_event_space_bijector` which returns a subclass of [`tfp.bijectors.Bijector`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Bijector) that maps R\*\*n to the distribution's event space. For example, the default bijector for the `Beta` distribution is [`tfp.bijectors.Sigmoid()`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Sigmoid), which maps the real line to `[0, 1]`, the support of the `Beta` distribution. The default bijector for the `CholeskyLKJ` distribution is [`tfp.bijectors.CorrelationCholesky`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/CorrelationCholesky), which maps R^(k \* (k-1) // 2) to the submanifold of k x k lower triangular matrices with ones along the diagonal. The purpose of `experimental_default_event_space_bijector` is to enable gradient descent in an unconstrained space for Variational Inference and Hamiltonian Monte Carlo methods. Some effort has been made to choose bijectors such that the tails of the distribution in the unconstrained space are between Gaussian and Exponential. For distributions with discrete event space, or for which TFP currently lacks a suitable bijector, this function returns `None`. | Args | | |---|---| | `*args` | Passed to implementation `_default_event_space_bijector`. | | `**kwargs` | Passed to implementation `_default_event_space_bijector`. | | Returns | | |---|---| | `event_space_bijector` | `Bijector` instance or `None`. | ### `experimental_fit` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1799-L1847) ``` @classmethod ``` Instantiates a distribution that maximizes the likelihood of `x`. | Args | | |---|---| | `value` | a `Tensor` valid sample from this distribution family. | | `sample_ndims` | Positive `int` Tensor number of leftmost dimensions of `value` that index i.i.d. samples. Default value: `1`. | | `validate_args` | Python `bool`, default `False`. When `True`, distribution parameters are checked for validity despite possibly degrading runtime performance. When `False`, invalid inputs may silently render incorrect outputs. Default value: `False`. | | `**init_kwargs` | Additional keyword arguments passed through to `cls.__init__`. These take precedence in case of collision with the fitted parameters; for example, `tfd.Normal.experimental_fit([1., 1.], scale=20.)` returns a Normal distribution with `scale=20.` rather than the maximum likelihood parameter `scale=0.`. | | Returns | | |---|---| | `maximum_likelihood_instance` | instance of `cls` with parameters that maximize the likelihood of `value`. | ### `experimental_from_mean_concentration` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/beta.py#L197-L229) ``` @classmethod ``` Constructs a Beta from its mean and total concentration. **Experimental: Naming, location of this API may change.** Total concentration, sometimes called "sample size", is the sum of the two concentration parameters (`concentration1` and `concentration0` in `__init__`). | Args | | |---|---| | `mean` | The mean of the constructed distribution. | | `total_concentration` | The sum of the two concentration parameters. Must be greater than 0. | | `**kwargs` | Other keyword arguments passed directly to `__init__`, e.g. `validate_args`. | | Returns | | |---|---| | `beta` | A distribution with the given parameterization. | ### `experimental_from_mean_variance` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/beta.py#L231-L258) ``` @classmethod ``` Constructs a Beta from its mean and variance. **Experimental: Naming, location of this API may change.** Variance must be less than `mean * (1. - mean)`, and in particular less than the maximal variance of 0.25, which occurs with `mean = 0.5`. | Args | | |---|---| | `mean` | The mean of the constructed distribution. | | `variance` | The variance of the constructed distribution. | | `**kwargs` | Other keyword arguments passed directly to `__init__`, e.g. `validate_args`. | | Returns | | |---|---| | `beta` | A distribution with the given parameterization. | ### `experimental_local_measure` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1872-L1914) ``` experimental_local_measure( value, backward_compat=False, **kwargs ) ``` Returns a log probability density together with a `TangentSpace`. A `TangentSpace` allows us to calculate the correct push-forward density when we apply a transformation to a `Distribution` on a strict submanifold of R^n (typically via a `Bijector` in the `TransformedDistribution` subclass). The density correction uses the basis of the tangent space. | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `backward_compat` | `bool` specifying whether to fall back to returning `FullSpace` as the tangent space, and representing R^n with the standard basis. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `log_prob` | a `Tensor` representing the log probability density, of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | | `tangent_space` | a `TangentSpace` object (by default `FullSpace`) representing the tangent space to the manifold at `value`. | | Raises | |---| | UnspecifiedTangentSpaceError if `backward_compat` is False and the `_experimental_tangent_space` attribute has not been defined. | ### `experimental_sample_and_log_prob` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1229-L1259) ``` experimental_sample_and_log_prob( sample_shape=(), seed=None, name='sample_and_log_prob', **kwargs ) ``` Samples from this distribution and returns the log density of the sample. The default implementation simply calls `sample` and `log_prob`: ``` def _sample_and_log_prob(self, sample_shape, seed, **kwargs): x = self.sample(sample_shape=sample_shape, seed=seed, **kwargs) return x, self.log_prob(x, **kwargs) ``` However, some subclasses may provide more efficient and/or numerically stable implementations. | Args | | |---|---| | `sample_shape` | integer `Tensor` desired shape of samples to draw. Default value: `()`. | | `seed` | PRNG seed; see [`tfp.random.sanitize_seed`](https://www.tensorflow.org/probability/api_docs/python/tfp/random/sanitize_seed) for details. Default value: `None`. | | `name` | name to give to the op. Default value: `'sample_and_log_prob'`. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `samples` | a `Tensor`, or structure of `Tensor`s, with prepended dimensions `sample_shape`. | | `log_prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `is_scalar_batch` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1156-L1168) ``` is_scalar_batch( name='is_scalar_batch' ) ``` Indicates that `batch_shape == []`. | Args | | |---|---| | `name` | Python `str` prepended to names of ops created by this function. | | Returns | | |---|---| | `is_scalar_batch` | `bool` scalar `Tensor`. | ### `is_scalar_event` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1142-L1154) ``` is_scalar_event( name='is_scalar_event' ) ``` Indicates that `event_shape == []`. | Args | | |---|---| | `name` | Python `str` prepended to names of ops created by this function. | | Returns | | |---|---| | `is_scalar_event` | `bool` scalar `Tensor`. | ### `kl_divergence` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1730-L1761) ``` kl_divergence( other, name='kl_divergence' ) ``` Computes the Kullback--Leibler divergence. Denote this distribution (`self`) by `p` and the `other` distribution by `q`. Assuming `p, q` are absolutely continuous with respect to reference measure `r`, the KL divergence is defined as: ``` KL[p, q] = E_p[log(p(X)/q(X))] = -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x) = H[p, q] - H[p] ``` where `F` denotes the support of the random variable `X ~ p`, `H[., .]` denotes (Shannon) cross entropy, and `H[.]` denotes (Shannon) entropy. `other` types with built-in registrations: `Beta` | Args | | |---|---| | `other` | [`tfp.distributions.Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution) instance. | | `name` | Python `str` prepended to names of ops created by this function. | | Returns | | |---|---| | `kl_divergence` | `self.dtype` `Tensor` with shape `[B1, ..., Bn]` representing `n` different calculations of the Kullback-Leibler divergence. | ### `log_cdf` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1373-L1395) ``` log_cdf( value, name='log_cdf', **kwargs ) ``` Log cumulative distribution function. Given random variable `X`, the cumulative distribution function `cdf` is: ``` log_cdf(x) := Log[ P[X <= x] ] ``` Often, a numerical approximation can be used for `log_cdf(x)` that yields a more accurate answer than simply taking the logarithm of the `cdf` when `x << -1`. Additional documentation from `Beta`: **Note:** `x` must have dtype `self.dtype` and be in `[0, 1].` It must have a shape compatible with `self.batch_shape()`. | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `logcdf` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `log_prob` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1275-L1287) ``` log_prob( value, name='log_prob', **kwargs ) ``` Log probability density/mass function. Additional documentation from `Beta`: **Note:** `x` must have dtype `self.dtype` and be in `[0, 1].` It must have a shape compatible with `self.batch_shape()`. | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `log_prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `log_survival_function` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1452-L1476) ``` log_survival_function( value, name='log_survival_function', **kwargs ) ``` Log survival function. Given random variable `X`, the survival function is defined: ``` log_survival_function(x) = Log[ P[X > x] ] = Log[ 1 - P[X <= x] ] = Log[ 1 - cdf(x) ] ``` Typically, different numerical approximations can be used for the log survival function, which are more accurate than `1 - cdf(x)` when `x >> 1`. | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | |---| | `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `mean` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1533-L1536) ``` mean( name='mean', **kwargs ) ``` Mean. ### `mode` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1692-L1695) ``` mode( name='mode', **kwargs ) ``` Mode. Additional documentation from `Beta`: **Note:** The mode is undefined when `concentration1 <= 1` or `concentration0 <= 1`. If `self.allow_nan_stats` is `True`, `NaN` is used for undefined modes. If `self.allow_nan_stats` is `False` an exception is raised when one or more modes are undefined. ### `param_shapes` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L701-L727) ``` @classmethod ``` Shapes of parameters given the desired shape of a call to `sample()`. (deprecated) **Deprecated:** THIS FUNCTION IS DEPRECATED. It will be removed after 2021-03-01. Instructions for updating: The `param_shapes` method of `tfd.Distribution` is deprecated; use `parameter_properties` instead. This is a class method that describes what key/value arguments are required to instantiate the given `Distribution` so that a particular shape is returned for that instance's call to `sample()`. Subclasses should override class method `_param_shapes`. | Args | | |---|---| | `sample_shape` | `Tensor` or python list/tuple. Desired shape of a call to `sample()`. | | `name` | name to prepend ops with. | | Returns | |---| | `dict` of parameter name to `Tensor` shapes. | ### `param_static_shapes` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L729-L769) ``` @classmethod ``` param\_shapes with static (i.e. `TensorShape`) shapes. (deprecated) **Deprecated:** THIS FUNCTION IS DEPRECATED. It will be removed after 2021-03-01. Instructions for updating: The `param_static_shapes` method of `tfd.Distribution` is deprecated; use `parameter_properties` instead. This is a class method that describes what key/value arguments are required to instantiate the given `Distribution` so that a particular shape is returned for that instance's call to `sample()`. Assumes that the sample's shape is known statically. Subclasses should override class method `_param_shapes` to return constant-valued tensors when constant values are fed. | Args | | |---|---| | `sample_shape` | `TensorShape` or python list/tuple. Desired shape of a call to `sample()`. | | Returns | |---| | `dict` of parameter name to `TensorShape`. | | Raises | | |---|---| | `ValueError` | if `sample_shape` is a `TensorShape` and is not fully defined. | ### `parameter_properties` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L655-L699) ``` @classmethod ``` Returns a dict mapping constructor arg names to property annotations. This dict should include an entry for each of the distribution's `Tensor`\-valued constructor arguments. Distribution subclasses are not required to implement `_parameter_properties`, so this method may raise `NotImplementedError`. Providing a `_parameter_properties` implementation enables several advanced features, including: - Distribution batch slicing (`sliced_distribution = distribution[i:j]`). - Automatic inference of `_batch_shape` and `_batch_shape_tensor`, which must otherwise be computed explicitly. - Automatic instantiation of the distribution within TFP's internal property tests. - Automatic construction of 'trainable' instances of the distribution using appropriate bijectors to avoid violating parameter constraints. This enables the distribution family to be used easily as a surrogate posterior in variational inference. In the future, parameter property annotations may enable additional functionality; for example, returning Distribution instances from [`tf.vectorized_map`](https://www.tensorflow.org/api_docs/python/tf/vectorized_map). | Args | | |---|---| | `dtype` | Optional float `dtype` to assume for continuous-valued parameters. Some constraining bijectors require advance knowledge of the dtype because certain constants (e.g., `tfb.Softplus.low`) must be instantiated with the same dtype as the values to be transformed. | | `num_classes` | Optional `int` `Tensor` number of classes to assume when inferring the shape of parameters for categorical-like distributions. Otherwise ignored. | | Returns | | |---|---| | `parameter_properties` | A `str ->`tfp.python.internal.parameter\_properties.ParameterProperties`dict mapping constructor argument names to`ParameterProperties\` instances. | | Raises | | |---|---| | `NotImplementedError` | if the distribution class does not implement `_parameter_properties`. | ### `prob` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1303-L1315) ``` prob( value, name='prob', **kwargs ) ``` Probability density/mass function. Additional documentation from `Beta`: **Note:** `x` must have dtype `self.dtype` and be in `[0, 1].` It must have a shape compatible with `self.batch_shape()`. | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `quantile` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1555-L1573) ``` quantile( value, name='quantile', **kwargs ) ``` Quantile function. Aka 'inverse cdf' or 'percent point function'. Given random variable `X` and `p in [0, 1]`, the `quantile` is: ``` quantile(p) := x such that P[X <= x] == p ``` | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `quantile` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `sample` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1189-L1205) ``` sample( sample_shape=(), seed=None, name='sample', **kwargs ) ``` Generate samples of the specified shape. Note that a call to `sample()` without arguments will generate a single sample. | Args | | |---|---| | `sample_shape` | 0D or 1D `int32` `Tensor`. Shape of the generated samples. | | `seed` | PRNG seed; see [`tfp.random.sanitize_seed`](https://www.tensorflow.org/probability/api_docs/python/tfp/random/sanitize_seed) for details. | | `name` | name to give to the op. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `samples` | a `Tensor` with prepended dimensions `sample_shape`. | ### `stddev` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1613-L1642) ``` stddev( name='stddev', **kwargs ) ``` Standard deviation. Standard deviation is defined as, ``` stddev = E[(X - E[X])**2]**0.5 ``` where `X` is the random variable associated with this distribution, `E` denotes expectation, and `stddev.shape = batch_shape + event_shape`. | Args | | |---|---| | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `stddev` | Floating-point `Tensor` with shape identical to `batch_shape + event_shape`, i.e., the same shape as `self.mean()`. | ### `survival_function` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1498-L1518) ``` survival_function( value, name='survival_function', **kwargs ) ``` Survival function. Given random variable `X`, the survival function is defined: ``` survival_function(x) = P[X > x] = 1 - P[X <= x] = 1 - cdf(x). ``` | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | |---| | `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `unnormalized_log_prob` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1335-L1357) ``` unnormalized_log_prob( value, name='unnormalized_log_prob', **kwargs ) ``` Potentially unnormalized log probability density/mass function. This function is similar to `log_prob`, but does not require that the return value be normalized. (Normalization here refers to the total integral of probability being one, as it should be by definition for any probability distribution.) This is useful, for example, for distributions where the normalization constant is difficult or expensive to compute. By default, this simply calls `log_prob`. | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `unnormalized_log_prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `variance` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1579-L1607) ``` variance( name='variance', **kwargs ) ``` Variance. Variance is defined as, ``` Var = E[(X - E[X])**2] ``` where `X` is the random variable associated with this distribution, `E` denotes expectation, and `Var.shape = batch_shape + event_shape`. | Args | | |---|---| | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `variance` | Floating-point `Tensor` with shape identical to `batch_shape + event_shape`, i.e., the same shape as `self.mean()`. | ### `with_name_scope` ``` @classmethod ``` Decorator to automatically enter the module name scope. ``` class MyModule(tf.Module): @tf.Module.with_name_scope def __call__(self, x): if not hasattr(self, 'w'): self.w = tf.Variable(tf.random.normal([x.shape[1], 3])) return tf.matmul(x, self.w) ``` Using the above module would produce [`tf.Variable`](https://www.tensorflow.org/api_docs/python/tf/Variable)s and [`tf.Tensor`](https://www.tensorflow.org/api_docs/python/tf/Tensor)s whose names included the module name: ``` mod = MyModule() mod(tf.ones([1, 2])) <tf.Tensor: shape=(1, 3), dtype=float32, numpy=..., dtype=float32)> mod.w <tf.Variable 'my_module/Variable:0' shape=(2, 3) dtype=float32, numpy=..., dtype=float32)> ``` | Args | | |---|---| | `method` | The method to wrap. | | Returns | |---| | The original method wrapped such that it enters the module's name scope. | ### `__getitem__` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L825-L852) ``` __getitem__( slices ) ``` Slices the batch axes of this distribution, returning a new instance. ``` b = tfd.Bernoulli(logits=tf.zeros([3, 5, 7, 9])) b.batch_shape # => [3, 5, 7, 9] b2 = b[:, tf.newaxis, ..., -2:, 1::2] b2.batch_shape # => [3, 1, 5, 2, 4] x = tf.random.normal([5, 3, 2, 2]) cov = tf.matmul(x, x, transpose_b=True) chol = tf.linalg.cholesky(cov) loc = tf.random.normal([4, 1, 3, 1]) mvn = tfd.MultivariateNormalTriL(loc, chol) mvn.batch_shape # => [4, 5, 3] mvn.event_shape # => [2] mvn2 = mvn[:, 3:, ..., ::-1, tf.newaxis] mvn2.batch_shape # => [4, 2, 3, 1] mvn2.event_shape # => [2] ``` | Args | | |---|---| | `slices` | slices from the \[\] operator | | Returns | | |---|---| | `dist` | A new `tfd.Distribution` instance with sliced parameters. | ### `__iter__` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L854-L855) ``` __iter__() ``` Was this helpful? 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Readable Markdown
Beta distribution. Inherits From: [`AutoCompositeTensorDistribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/AutoCompositeTensorDistribution), [`Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution), [`AutoCompositeTensor`](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/AutoCompositeTensor) ``` tfp.distributions.Beta( concentration1, concentration0, validate_args=False, allow_nan_stats=True, force_probs_to_zero_outside_support=False, name='Beta' ) ``` The Beta distribution is defined over the `(0, 1)` interval using parameters `concentration1` (aka 'alpha') and `concentration0` (aka 'beta'). #### Mathematical Details The probability density function (pdf) is, ``` pdf(x; alpha, beta) = x**(alpha - 1) (1 - x)**(beta - 1) / Z Z = Gamma(alpha) Gamma(beta) / Gamma(alpha + beta) ``` where: - `concentration1 = alpha`, - `concentration0 = beta`, - `Z` is the normalization constant, and, - `Gamma` is the [gamma function](https://en.wikipedia.org/wiki/Gamma_function). The concentration parameters represent mean total counts of a `1` or a `0`, i.e., ``` concentration1 = alpha = mean * total_concentration concentration0 = beta = (1. - mean) * total_concentration ``` where `mean` in `(0, 1)` and `total_concentration` is a positive real number representing a mean `total_count = concentration1 + concentration0`. Distribution parameters are automatically broadcast in all functions; see examples for details. Samples of this distribution are reparameterized (pathwise differentiable). The derivatives are computed using the approach described in the paper [Michael Figurnov, Shakir Mohamed, Andriy Mnih. Implicit Reparameterization Gradients, 2018](https://arxiv.org/abs/1805.08498) #### Examples ``` import tensorflow_probability as tfp tfd = tfp.distributions # Create a batch of three Beta distributions. alpha = [1, 2, 3] beta = [1, 2, 3] dist = tfd.Beta(alpha, beta) dist.sample([4, 5]) # Shape [4, 5, 3] # `x` has three batch entries, each with two samples. x = [[.1, .4, .5], [.2, .3, .5]] # Calculate the probability of each pair of samples under the corresponding # distribution in `dist`. dist.prob(x) # Shape [2, 3] # Define an equivalent Beta distribution parameterized by `mean` and # `total_concentration`: dist = tfd.Beta.experimental_from_mean_concentration( mean=0.5, total_concentration=alpha+beta) ``` ``` # Create batch_shape=[2, 3] via parameter broadcast: alpha = [[1.], [2]] # Shape [2, 1] beta = [3., 4, 5] # Shape [3] dist = tfd.Beta(alpha, beta) # alpha broadcast as: [[1., 1, 1,], # [2, 2, 2]] # beta broadcast as: [[3., 4, 5], # [3, 4, 5]] # batch_Shape [2, 3] dist.sample([4, 5]) # Shape [4, 5, 2, 3] x = [.2, .3, .5] # x will be broadcast as [[.2, .3, .5], # [.2, .3, .5]], # thus matching batch_shape [2, 3]. dist.prob(x) # Shape [2, 3] ``` Compute the gradients of samples w.r.t. the parameters: ``` alpha = tf.constant(1.0) beta = tf.constant(2.0) dist = tfd.Beta(alpha, beta) samples = dist.sample(5) # Shape [5] loss = tf.reduce_mean(tf.square(samples)) # Arbitrary loss function # Unbiased stochastic gradients of the loss function grads = tf.gradients(loss, [alpha, beta]) ``` | Args | | |---|---| | `concentration1` | Positive floating-point `Tensor` indicating mean number of successes; aka 'alpha'. | | `concentration0` | Positive floating-point `Tensor` indicating mean number of failures; aka 'beta'. | | `validate_args` | Python `bool`, default `False`. When `True` distribution parameters are checked for validity despite possibly degrading runtime performance. When `False` invalid inputs may silently render incorrect outputs. | | `allow_nan_stats` | Python `bool`, default `True`. When `True`, statistics (e.g., mean, mode, variance) use the value '`NaN`' to indicate the result is undefined. When `False`, an exception is raised if one or more of the statistic's batch members are undefined. | | `force_probs_to_zero_outside_support` | If `True`, force `prob(x) == 0` and `log_prob(x) == -inf` for values of x outside the distribution support. | | `name` | Python `str` name prefixed to Ops created by this class. | | Attributes | | |---|---| | `allow_nan_stats` | Python `bool` describing behavior when a stat is undefined. Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E\[(X - mean)\*\*2\] is also undefined. | | `batch_shape` | Shape of a single sample from a single event index as a `TensorShape`. May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution. | | `concentration0` | Concentration parameter associated with a `0` outcome. | | `concentration1` | Concentration parameter associated with a `1` outcome. | | `dtype` | The `DType` of `Tensor`s handled by this `Distribution`. | | `event_shape` | Shape of a single sample from a single batch as a `TensorShape`. May be partially defined or unknown. | | `experimental_shard_axis_names` | The list or structure of lists of active shard axis names. | | `force_probs_to_zero_outside_support` | | | `name` | Name prepended to all ops created by this `Distribution`. | | `name_scope` | Returns a [`tf.name_scope`](https://www.tensorflow.org/api_docs/python/tf/name_scope) instance for this class. | | `non_trainable_variables` | Sequence of non-trainable variables owned by this module and its submodules. | | `parameters` | Dictionary of parameters used to instantiate this `Distribution`. | | `reparameterization_type` | Describes how samples from the distribution are reparameterized. Currently this is one of the static instances `tfd.FULLY_REPARAMETERIZED` or `tfd.NOT_REPARAMETERIZED`. | | `submodules` | Sequence of all sub-modules. Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on). | | `trainable_variables` | Sequence of trainable variables owned by this module and its submodules. | | `validate_args` | Python `bool` indicating possibly expensive checks are enabled. | | `variables` | Sequence of variables owned by this module and its submodules. | ## Methods ### `batch_shape_tensor` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L992-L1030) ``` batch_shape_tensor( name='batch_shape_tensor' ) ``` Shape of a single sample from a single event index as a 1-D `Tensor`. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution. | Args | | |---|---| | `name` | name to give to the op | | Returns | | |---|---| | `batch_shape` | `Tensor`. | ### `cdf` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1411-L1429) ``` cdf( value, name='cdf', **kwargs ) ``` Cumulative distribution function. Given random variable `X`, the cumulative distribution function `cdf` is: ``` cdf(x) := P[X <= x] ``` Additional documentation from `Beta`: | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `cdf` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `copy` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L896-L924) ``` copy( **override_parameters_kwargs ) ``` Creates a deep copy of the distribution. | Args | | |---|---| | `**override_parameters_kwargs` | String/value dictionary of initialization arguments to override with new values. | | Returns | | |---|---| | `distribution` | A new instance of `type(self)` initialized from the union of self.parameters and override\_parameters\_kwargs, i.e., `dict(self.parameters, **override_parameters_kwargs)`. | ### `covariance` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1648-L1686) ``` covariance( name='covariance', **kwargs ) ``` Covariance. Covariance is (possibly) defined only for non-scalar-event distributions. For example, for a length-`k`, vector-valued distribution, it is calculated as, ``` Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])] ``` where `Cov` is a (batch of) `k x k` matrix, `0 <= (i, j) < k`, and `E` denotes expectation. Alternatively, for non-vector, multivariate distributions (e.g., matrix-valued, Wishart), `Covariance` shall return a (batch of) matrices under some vectorization of the events, i.e., ``` Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above] ``` where `Cov` is a (batch of) `k' x k'` matrices, `0 <= (i, j) < k' = reduce_prod(event_shape)`, and `Vec` is some function mapping indices of this distribution's event dimensions to indices of a length-`k'` vector. | Args | | |---|---| | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `covariance` | Floating-point `Tensor` with shape `[B1, ..., Bn, k', k']` where the first `n` dimensions are batch coordinates and `k' = reduce_prod(self.event_shape)`. | ### `cross_entropy` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1701-L1724) ``` cross_entropy( other, name='cross_entropy' ) ``` Computes the (Shannon) cross entropy. Denote this distribution (`self`) by `P` and the `other` distribution by `Q`. Assuming `P, Q` are absolutely continuous with respect to one another and permit densities `p(x) dr(x)` and `q(x) dr(x)`, (Shannon) cross entropy is defined as: ``` H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x) ``` where `F` denotes the support of the random variable `X ~ P`. `other` types with built-in registrations: `Beta` | Args | | |---|---| | `other` | [`tfp.distributions.Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution) instance. | | `name` | Python `str` prepended to names of ops created by this function. | | Returns | | |---|---| | `cross_entropy` | `self.dtype` `Tensor` with shape `[B1, ..., Bn]` representing `n` different calculations of (Shannon) cross entropy. | ### `entropy` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1524-L1527) ``` entropy( name='entropy', **kwargs ) ``` Shannon entropy in nats. ### `event_shape_tensor` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1099-L1125) ``` event_shape_tensor( name='event_shape_tensor' ) ``` Shape of a single sample from a single batch as a 1-D int32 `Tensor`. | Args | | |---|---| | `name` | name to give to the op | | Returns | | |---|---| | `event_shape` | `Tensor`. | ### `experimental_default_event_space_bijector` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1768-L1797) ``` experimental_default_event_space_bijector( *args, **kwargs ) ``` Bijector mapping the reals (R\*\*n) to the event space of the distribution. Distributions with continuous support may implement `_default_event_space_bijector` which returns a subclass of [`tfp.bijectors.Bijector`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Bijector) that maps R\*\*n to the distribution's event space. For example, the default bijector for the `Beta` distribution is [`tfp.bijectors.Sigmoid()`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Sigmoid), which maps the real line to `[0, 1]`, the support of the `Beta` distribution. The default bijector for the `CholeskyLKJ` distribution is [`tfp.bijectors.CorrelationCholesky`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/CorrelationCholesky), which maps R^(k \* (k-1) // 2) to the submanifold of k x k lower triangular matrices with ones along the diagonal. The purpose of `experimental_default_event_space_bijector` is to enable gradient descent in an unconstrained space for Variational Inference and Hamiltonian Monte Carlo methods. Some effort has been made to choose bijectors such that the tails of the distribution in the unconstrained space are between Gaussian and Exponential. For distributions with discrete event space, or for which TFP currently lacks a suitable bijector, this function returns `None`. | Args | | |---|---| | `*args` | Passed to implementation `_default_event_space_bijector`. | | `**kwargs` | Passed to implementation `_default_event_space_bijector`. | | Returns | | |---|---| | `event_space_bijector` | `Bijector` instance or `None`. | ### `experimental_fit` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1799-L1847) ``` @classmethod ``` Instantiates a distribution that maximizes the likelihood of `x`. | Args | | |---|---| | `value` | a `Tensor` valid sample from this distribution family. | | `sample_ndims` | Positive `int` Tensor number of leftmost dimensions of `value` that index i.i.d. samples. Default value: `1`. | | `validate_args` | Python `bool`, default `False`. When `True`, distribution parameters are checked for validity despite possibly degrading runtime performance. When `False`, invalid inputs may silently render incorrect outputs. Default value: `False`. | | `**init_kwargs` | Additional keyword arguments passed through to `cls.__init__`. These take precedence in case of collision with the fitted parameters; for example, `tfd.Normal.experimental_fit([1., 1.], scale=20.)` returns a Normal distribution with `scale=20.` rather than the maximum likelihood parameter `scale=0.`. | | Returns | | |---|---| | `maximum_likelihood_instance` | instance of `cls` with parameters that maximize the likelihood of `value`. | ### `experimental_from_mean_concentration` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/beta.py#L197-L229) ``` @classmethod ``` Constructs a Beta from its mean and total concentration. **Experimental: Naming, location of this API may change.** Total concentration, sometimes called "sample size", is the sum of the two concentration parameters (`concentration1` and `concentration0` in `__init__`). | Args | | |---|---| | `mean` | The mean of the constructed distribution. | | `total_concentration` | The sum of the two concentration parameters. Must be greater than 0. | | `**kwargs` | Other keyword arguments passed directly to `__init__`, e.g. `validate_args`. | | Returns | | |---|---| | `beta` | A distribution with the given parameterization. | ### `experimental_from_mean_variance` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/beta.py#L231-L258) ``` @classmethod ``` Constructs a Beta from its mean and variance. **Experimental: Naming, location of this API may change.** Variance must be less than `mean * (1. - mean)`, and in particular less than the maximal variance of 0.25, which occurs with `mean = 0.5`. | Args | | |---|---| | `mean` | The mean of the constructed distribution. | | `variance` | The variance of the constructed distribution. | | `**kwargs` | Other keyword arguments passed directly to `__init__`, e.g. `validate_args`. | | Returns | | |---|---| | `beta` | A distribution with the given parameterization. | ### `experimental_local_measure` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1872-L1914) ``` experimental_local_measure( value, backward_compat=False, **kwargs ) ``` Returns a log probability density together with a `TangentSpace`. A `TangentSpace` allows us to calculate the correct push-forward density when we apply a transformation to a `Distribution` on a strict submanifold of R^n (typically via a `Bijector` in the `TransformedDistribution` subclass). The density correction uses the basis of the tangent space. | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `backward_compat` | `bool` specifying whether to fall back to returning `FullSpace` as the tangent space, and representing R^n with the standard basis. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `log_prob` | a `Tensor` representing the log probability density, of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | | `tangent_space` | a `TangentSpace` object (by default `FullSpace`) representing the tangent space to the manifold at `value`. | | Raises | |---| | UnspecifiedTangentSpaceError if `backward_compat` is False and the `_experimental_tangent_space` attribute has not been defined. | ### `experimental_sample_and_log_prob` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1229-L1259) ``` experimental_sample_and_log_prob( sample_shape=(), seed=None, name='sample_and_log_prob', **kwargs ) ``` Samples from this distribution and returns the log density of the sample. The default implementation simply calls `sample` and `log_prob`: ``` def _sample_and_log_prob(self, sample_shape, seed, **kwargs): x = self.sample(sample_shape=sample_shape, seed=seed, **kwargs) return x, self.log_prob(x, **kwargs) ``` However, some subclasses may provide more efficient and/or numerically stable implementations. | Args | | |---|---| | `sample_shape` | integer `Tensor` desired shape of samples to draw. Default value: `()`. | | `seed` | PRNG seed; see [`tfp.random.sanitize_seed`](https://www.tensorflow.org/probability/api_docs/python/tfp/random/sanitize_seed) for details. Default value: `None`. | | `name` | name to give to the op. Default value: `'sample_and_log_prob'`. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `samples` | a `Tensor`, or structure of `Tensor`s, with prepended dimensions `sample_shape`. | | `log_prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `is_scalar_batch` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1156-L1168) ``` is_scalar_batch( name='is_scalar_batch' ) ``` Indicates that `batch_shape == []`. | Args | | |---|---| | `name` | Python `str` prepended to names of ops created by this function. | | Returns | | |---|---| | `is_scalar_batch` | `bool` scalar `Tensor`. | ### `is_scalar_event` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1142-L1154) ``` is_scalar_event( name='is_scalar_event' ) ``` Indicates that `event_shape == []`. | Args | | |---|---| | `name` | Python `str` prepended to names of ops created by this function. | | Returns | | |---|---| | `is_scalar_event` | `bool` scalar `Tensor`. | ### `kl_divergence` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1730-L1761) ``` kl_divergence( other, name='kl_divergence' ) ``` Computes the Kullback--Leibler divergence. Denote this distribution (`self`) by `p` and the `other` distribution by `q`. Assuming `p, q` are absolutely continuous with respect to reference measure `r`, the KL divergence is defined as: ``` KL[p, q] = E_p[log(p(X)/q(X))] = -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x) = H[p, q] - H[p] ``` where `F` denotes the support of the random variable `X ~ p`, `H[., .]` denotes (Shannon) cross entropy, and `H[.]` denotes (Shannon) entropy. `other` types with built-in registrations: `Beta` | Args | | |---|---| | `other` | [`tfp.distributions.Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution) instance. | | `name` | Python `str` prepended to names of ops created by this function. | | Returns | | |---|---| | `kl_divergence` | `self.dtype` `Tensor` with shape `[B1, ..., Bn]` representing `n` different calculations of the Kullback-Leibler divergence. | ### `log_cdf` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1373-L1395) ``` log_cdf( value, name='log_cdf', **kwargs ) ``` Log cumulative distribution function. Given random variable `X`, the cumulative distribution function `cdf` is: ``` log_cdf(x) := Log[ P[X <= x] ] ``` Often, a numerical approximation can be used for `log_cdf(x)` that yields a more accurate answer than simply taking the logarithm of the `cdf` when `x << -1`. Additional documentation from `Beta`: | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `logcdf` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `log_prob` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1275-L1287) ``` log_prob( value, name='log_prob', **kwargs ) ``` Log probability density/mass function. Additional documentation from `Beta`: | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `log_prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `log_survival_function` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1452-L1476) ``` log_survival_function( value, name='log_survival_function', **kwargs ) ``` Log survival function. Given random variable `X`, the survival function is defined: ``` log_survival_function(x) = Log[ P[X > x] ] = Log[ 1 - P[X <= x] ] = Log[ 1 - cdf(x) ] ``` Typically, different numerical approximations can be used for the log survival function, which are more accurate than `1 - cdf(x)` when `x >> 1`. | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | |---| | `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `mean` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1533-L1536) ``` mean( name='mean', **kwargs ) ``` Mean. ### `mode` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1692-L1695) ``` mode( name='mode', **kwargs ) ``` Mode. Additional documentation from `Beta`: ### `param_shapes` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L701-L727) ``` @classmethod ``` Shapes of parameters given the desired shape of a call to `sample()`. (deprecated) This is a class method that describes what key/value arguments are required to instantiate the given `Distribution` so that a particular shape is returned for that instance's call to `sample()`. Subclasses should override class method `_param_shapes`. | Args | | |---|---| | `sample_shape` | `Tensor` or python list/tuple. Desired shape of a call to `sample()`. | | `name` | name to prepend ops with. | | Returns | |---| | `dict` of parameter name to `Tensor` shapes. | ### `param_static_shapes` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L729-L769) ``` @classmethod ``` param\_shapes with static (i.e. `TensorShape`) shapes. (deprecated) This is a class method that describes what key/value arguments are required to instantiate the given `Distribution` so that a particular shape is returned for that instance's call to `sample()`. Assumes that the sample's shape is known statically. Subclasses should override class method `_param_shapes` to return constant-valued tensors when constant values are fed. | Args | | |---|---| | `sample_shape` | `TensorShape` or python list/tuple. Desired shape of a call to `sample()`. | | Returns | |---| | `dict` of parameter name to `TensorShape`. | | Raises | | |---|---| | `ValueError` | if `sample_shape` is a `TensorShape` and is not fully defined. | ### `parameter_properties` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L655-L699) ``` @classmethod ``` Returns a dict mapping constructor arg names to property annotations. This dict should include an entry for each of the distribution's `Tensor`\-valued constructor arguments. Distribution subclasses are not required to implement `_parameter_properties`, so this method may raise `NotImplementedError`. Providing a `_parameter_properties` implementation enables several advanced features, including: - Distribution batch slicing (`sliced_distribution = distribution[i:j]`). - Automatic inference of `_batch_shape` and `_batch_shape_tensor`, which must otherwise be computed explicitly. - Automatic instantiation of the distribution within TFP's internal property tests. - Automatic construction of 'trainable' instances of the distribution using appropriate bijectors to avoid violating parameter constraints. This enables the distribution family to be used easily as a surrogate posterior in variational inference. In the future, parameter property annotations may enable additional functionality; for example, returning Distribution instances from [`tf.vectorized_map`](https://www.tensorflow.org/api_docs/python/tf/vectorized_map). | Args | | |---|---| | `dtype` | Optional float `dtype` to assume for continuous-valued parameters. Some constraining bijectors require advance knowledge of the dtype because certain constants (e.g., `tfb.Softplus.low`) must be instantiated with the same dtype as the values to be transformed. | | `num_classes` | Optional `int` `Tensor` number of classes to assume when inferring the shape of parameters for categorical-like distributions. Otherwise ignored. | | Returns | | |---|---| | `parameter_properties` | A `str ->`tfp.python.internal.parameter\_properties.ParameterProperties`dict mapping constructor argument names to`ParameterProperties\` instances. | | Raises | | |---|---| | `NotImplementedError` | if the distribution class does not implement `_parameter_properties`. | ### `prob` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1303-L1315) ``` prob( value, name='prob', **kwargs ) ``` Probability density/mass function. Additional documentation from `Beta`: | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `quantile` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1555-L1573) ``` quantile( value, name='quantile', **kwargs ) ``` Quantile function. Aka 'inverse cdf' or 'percent point function'. Given random variable `X` and `p in [0, 1]`, the `quantile` is: ``` quantile(p) := x such that P[X <= x] == p ``` | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `quantile` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `sample` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1189-L1205) ``` sample( sample_shape=(), seed=None, name='sample', **kwargs ) ``` Generate samples of the specified shape. Note that a call to `sample()` without arguments will generate a single sample. | Args | | |---|---| | `sample_shape` | 0D or 1D `int32` `Tensor`. Shape of the generated samples. | | `seed` | PRNG seed; see [`tfp.random.sanitize_seed`](https://www.tensorflow.org/probability/api_docs/python/tfp/random/sanitize_seed) for details. | | `name` | name to give to the op. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `samples` | a `Tensor` with prepended dimensions `sample_shape`. | ### `stddev` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1613-L1642) ``` stddev( name='stddev', **kwargs ) ``` Standard deviation. Standard deviation is defined as, ``` stddev = E[(X - E[X])**2]**0.5 ``` where `X` is the random variable associated with this distribution, `E` denotes expectation, and `stddev.shape = batch_shape + event_shape`. | Args | | |---|---| | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `stddev` | Floating-point `Tensor` with shape identical to `batch_shape + event_shape`, i.e., the same shape as `self.mean()`. | ### `survival_function` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1498-L1518) ``` survival_function( value, name='survival_function', **kwargs ) ``` Survival function. Given random variable `X`, the survival function is defined: ``` survival_function(x) = P[X > x] = 1 - P[X <= x] = 1 - cdf(x). ``` | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | |---| | `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `unnormalized_log_prob` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1335-L1357) ``` unnormalized_log_prob( value, name='unnormalized_log_prob', **kwargs ) ``` Potentially unnormalized log probability density/mass function. This function is similar to `log_prob`, but does not require that the return value be normalized. (Normalization here refers to the total integral of probability being one, as it should be by definition for any probability distribution.) This is useful, for example, for distributions where the normalization constant is difficult or expensive to compute. By default, this simply calls `log_prob`. | Args | | |---|---| | `value` | `float` or `double` `Tensor`. | | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `unnormalized_log_prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. | ### `variance` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1579-L1607) ``` variance( name='variance', **kwargs ) ``` Variance. Variance is defined as, ``` Var = E[(X - E[X])**2] ``` where `X` is the random variable associated with this distribution, `E` denotes expectation, and `Var.shape = batch_shape + event_shape`. | Args | | |---|---| | `name` | Python `str` prepended to names of ops created by this function. | | `**kwargs` | Named arguments forwarded to subclass implementation. | | Returns | | |---|---| | `variance` | Floating-point `Tensor` with shape identical to `batch_shape + event_shape`, i.e., the same shape as `self.mean()`. | ### `with_name_scope` ``` @classmethod ``` Decorator to automatically enter the module name scope. ``` class MyModule(tf.Module): @tf.Module.with_name_scope def __call__(self, x): if not hasattr(self, 'w'): self.w = tf.Variable(tf.random.normal([x.shape[1], 3])) return tf.matmul(x, self.w) ``` Using the above module would produce [`tf.Variable`](https://www.tensorflow.org/api_docs/python/tf/Variable)s and [`tf.Tensor`](https://www.tensorflow.org/api_docs/python/tf/Tensor)s whose names included the module name: ``` mod = MyModule() mod(tf.ones([1, 2])) <tf.Tensor: shape=(1, 3), dtype=float32, numpy=..., dtype=float32)> mod.w <tf.Variable 'my_module/Variable:0' shape=(2, 3) dtype=float32, numpy=..., dtype=float32)> ``` | Args | | |---|---| | `method` | The method to wrap. | | Returns | |---| | The original method wrapped such that it enters the module's name scope. | ### `__getitem__` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L825-L852) ``` __getitem__( slices ) ``` Slices the batch axes of this distribution, returning a new instance. ``` b = tfd.Bernoulli(logits=tf.zeros([3, 5, 7, 9])) b.batch_shape # => [3, 5, 7, 9] b2 = b[:, tf.newaxis, ..., -2:, 1::2] b2.batch_shape # => [3, 1, 5, 2, 4] x = tf.random.normal([5, 3, 2, 2]) cov = tf.matmul(x, x, transpose_b=True) chol = tf.linalg.cholesky(cov) loc = tf.random.normal([4, 1, 3, 1]) mvn = tfd.MultivariateNormalTriL(loc, chol) mvn.batch_shape # => [4, 5, 3] mvn.event_shape # => [2] mvn2 = mvn[:, 3:, ..., ::-1, tf.newaxis] mvn2.batch_shape # => [4, 2, 3, 1] mvn2.event_shape # => [2] ``` | Args | | |---|---| | `slices` | slices from the \[\] operator | | Returns | | |---|---| | `dist` | A new `tfd.Distribution` instance with sliced parameters. | ### `__iter__` [View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L854-L855) ``` __iter__() ```
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