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| Boilerpipe Text | This course introduces the Bayesian approach to statistics, starting with the concept of probability and moving to the analysis of data. We will learn about the philosophy of the Bayesian approach as well as how to implement it for common types of data. We will compare the Bayesian approach to the more commonly-taught Frequentist approach, and see some of the benefits of the Bayesian approach. In particular, the Bayesian approach allows for better accounting of uncertainty, results that have more intuitive and interpretable meaning, and more explicit statements of assumptions. This course combines lecture videos, computer demonstrations, readings, exercises, and discussion boards to create an active learning experience. For computing, you have the choice of using Microsoft Excel or the open-source, freely available statistical package R, with equivalent content for both options. The lectures provide some of the basic mathematical development as well as explanations of philosophy and interpretation. Completion of this course will give you an understanding of the concepts of the Bayesian approach, understanding the key differences between Bayesian and Frequentist approaches, and the ability to do basic data analyses. |
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## Bayesian Statistics: From Concept to Data Analysis
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# Bayesian Statistics: From Concept to Data Analysis
This course is part of [Bayesian Statistics Specialization](https://www.coursera.org/specializations/bayesian-statistics)

Instructor: [Herbert Lee](https://www.coursera.org/instructor/ucsc)
**159,482** already enrolled
Included with
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[4 modules](https://www.coursera.org/learn/bayesian-statistics#modules)
Gain insight into a topic and learn the fundamentals.
4\.6
3,227 reviews
Intermediate level
Recommended experience
## Recommended experience
Intermediate level
Some experience with statistical data analysis is recommended.
OK
Flexible schedule
1 week at 10 hours a week
Learn at your own pace
92%
Most learners liked this course
***
[4 modules](https://www.coursera.org/learn/bayesian-statistics#modules)
Gain insight into a topic and learn the fundamentals.
4\.6
3,227 reviews
Intermediate level
Recommended experience
## Recommended experience
Intermediate level
Some experience with statistical data analysis is recommended.
OK
Flexible schedule
1 week at 10 hours a week
Learn at your own pace
92%
Most learners liked this course
- [About](https://www.coursera.org/learn/bayesian-statistics#about)
- [Outcomes](https://www.coursera.org/learn/bayesian-statistics#outcomes)
- [Modules](https://www.coursera.org/learn/bayesian-statistics#modules)
- [Recommendations](https://www.coursera.org/learn/bayesian-statistics#recommendations)
- [Testimonials](https://www.coursera.org/learn/bayesian-statistics#testimonials)
- [Reviews](https://www.coursera.org/learn/bayesian-statistics#reviews)
## What you'll learn
- Describe & apply the Bayesian approach to statistics.
- Explain the key differences between Bayesian and Frequentist approaches.
- Master the basics of the R computing environment.
## Skills you'll gain
- [Probability](https://www.coursera.org/courses?query=probability)
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## Build your subject-matter expertise
This course is part of the [Bayesian Statistics Specialization](https://www.coursera.org/specializations/bayesian-statistics)
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## There are 4 modules in this course
This course introduces the Bayesian approach to statistics, starting with the concept of probability and moving to the analysis of data. We will learn about the philosophy of the Bayesian approach as well as how to implement it for common types of data. We will compare the Bayesian approach to the more commonly-taught Frequentist approach, and see some of the benefits of the Bayesian approach. In particular, the Bayesian approach allows for better accounting of uncertainty, results that have more intuitive and interpretable meaning, and more explicit statements of assumptions. This course combines lecture videos, computer demonstrations, readings, exercises, and discussion boards to create an active learning experience. For computing, you have the choice of using Microsoft Excel or the open-source, freely available statistical package R, with equivalent content for both options. The lectures provide some of the basic mathematical development as well as explanations of philosophy and interpretation. Completion of this course will give you an understanding of the concepts of the Bayesian approach, understanding the key differences between Bayesian and Frequentist approaches, and the ability to do basic data analyses.
### Probability and Bayes' Theorem
Module 1ā¢3 hours to complete
Module details
In this module, we review the basics of probability and Bayesā theorem. In Lesson 1, we introduce the different paradigms or definitions of probability and discuss why probability provides a coherent framework for dealing with uncertainty. In Lesson 2, we review the rules of conditional probability and introduce Bayesā theorem. Lesson 3 reviews common probability distributions for discrete and continuous random variables.
#### What's included
8 videos4 readings5 assignments
Show info about module content
##### 8 videosā¢Total 38 minutes
- š„ Course introductionā¢4 minutes
- š„ Lesson 1.1 Classical and frequentist probabilityā¢6 minutes
- š„ Lesson 1.2 Bayesian probability and coherenceā¢3 minutes
- š„ Lesson 2.1 Conditional probabilityā¢4 minutes
- š„ Lesson 2.2 Bayes' theoremā¢6 minutes
- š„ Lesson 3.1 Bernoulli and binomial distributionsā¢5 minutes
- š„ Lesson 3.2 Uniform distributionā¢5 minutes
- š„ Lesson 3.3 Exponential and normal distributionsā¢3 minutes
##### 4 readingsā¢Total 36 minutes
- š Module 1 objectives, assignments, and supplementary materialsā¢3 minutes
- š Background for Lesson 1ā¢10 minutes
- š Supplementary material for Lesson 2ā¢3 minutes
- š Supplementary material for Lesson 3ā¢20 minutes
##### 5 assignmentsā¢Total 97 minutes
- āļø Lesson 1: Demonstrate your knowledgeā¢30 minutes
- āļø Lesson 2: Demonstrate your knowledgeā¢12 minutes
- āļø Lesson 3.1: Demonstrate your knowledgeā¢30 minutes
- āļø Lesson 3.2-3.3: Demonstrate your knowledgeā¢10 minutes
- āļø Module 1 Honors ā¢15 minutes
### Statistical Inference
Module 2ā¢3 hours to complete
Module details
This module introduces concepts of statistical inference from both frequentist and Bayesian perspectives. Lesson 4 takes the frequentist view, demonstrating maximum likelihood estimation and confidence intervals for binomial data. Lesson 5 introduces the fundamentals of Bayesian inference. Beginning with a binomial likelihood and prior probabilities for simple hypotheses, you will learn how to use Bayesā theorem to update the prior with data to obtain posterior probabilities. This framework is extended with the continuous version of Bayes theorem to estimate continuous model parameters, and calculate posterior probabilities and credible intervals.
#### What's included
11 videos5 readings4 assignments
Show info about module content
##### 11 videosā¢Total 59 minutes
- š„ Lesson 4.1 Confidence intervalsā¢5 minutes
- š„ Lesson 4.2 Likelihood function and maximum likelihoodā¢7 minutes
- š„ Lesson 4.3 Computing the MLEā¢3 minutes
- š„ Lesson 4.4 Computing the MLE: examplesā¢4 minutes
- š„ Introduction to Rā¢7 minutes
- š„ Plotting the likelihood in Rā¢5 minutes
- š„ Plotting the likelihood in Excelā¢5 minutes
- š„ Lesson 5.1 Inference example: frequentistā¢4 minutes
- š„ Lesson 5.2 Inference example: Bayesianā¢7 minutes
- š„ Lesson 5.3 Continuous version of Bayes' theoremā¢4 minutes
- š„ Lesson 5.4 Posterior intervalsā¢8 minutes
##### 5 readingsā¢Total 38 minutes
- š Module 2 objectives, assignments, and supplementary materialsā¢3 minutes
- š Background for Lesson 4ā¢10 minutes
- š Supplementary material for Lesson 4ā¢5 minutes
- š Background for Lesson 5ā¢10 minutes
- š Supplementary material for Lesson 5ā¢10 minutes
##### 4 assignmentsā¢Total 74 minutes
- āļø Lesson 4: Demonstrate your knowledgeā¢8 minutes
- āļø Lesson 5.1-5.2: Demonstrate your knowledgeā¢30 minutes
- āļø Lesson 5.3-5.4: Demonstrate your knowledgeā¢30 minutes
- āļø Module 2 Honors ā¢6 minutes
### Priors and Models for Discrete Data
Module 3ā¢2 hours to complete
Module details
In this module, you will learn methods for selecting prior distributions and building models for discrete data. Lesson 6 introduces prior selection and predictive distributions as a means of evaluating priors. Lesson 7 demonstrates Bayesian analysis of Bernoulli data and introduces the computationally convenient concept of conjugate priors. Lesson 8 builds a conjugate model for Poisson data and discusses strategies for selection of prior hyperparameters.
#### What's included
9 videos2 readings4 assignments
Show info about module content
##### 9 videosā¢Total 66 minutes
- š„ Lesson 6.1 Priors and prior predictive distributionsā¢4 minutes
- š„ Lesson 6.2 Prior predictive: binomial exampleā¢5 minutes
- š„ Lesson 6.3 Posterior predictive distributionā¢4 minutes
- š„ Lesson 7.1 Bernoulli/binomial likelihood with uniform priorā¢4 minutes
- š„ Lesson 7.2 Conjugate priorsā¢5 minutes
- š„ Lesson 7.3 Posterior mean and effective sample sizeā¢7 minutes
- š„ Data analysis example in Rā¢13 minutes
- š„ Data analysis example in Excelā¢16 minutes
- š„ Lesson 8.1 Poisson dataā¢8 minutes
##### 2 readingsā¢Total 13 minutes
- š Module 3 objectives, assignments, and supplementary materialsā¢3 minutes
- š R and Excel code from example analysisā¢10 minutes
##### 4 assignmentsā¢Total 68 minutes
- āļø Lesson 6: Demonstrate your knowledgeā¢30 minutes
- āļø Lesson 7: Demonstrate your knowledgeā¢15 minutes
- āļø Lesson 8: Demonstrate your knowledgeā¢15 minutes
- āļø Module 3 Honors ā¢8 minutes
### Models for Continuous Data
Module 4ā¢3 hours to complete
Module details
This module covers conjugate and objective Bayesian analysis for continuous data. Lesson 9 presents the conjugate model for exponentially distributed data. Lesson 10 discusses models for normally distributed data, which play a central role in statistics. In Lesson 11, we return to prior selection and discuss āobjectiveā or ānon-informativeā priors. Lesson 12 presents Bayesian linear regression with non-informative priors, which yield results comparable to those of classical regression.
#### What's included
9 videos5 readings5 assignments
Show info about module content
##### 9 videosā¢Total 69 minutes
- š„ Lesson 9.1 Exponential dataā¢4 minutes
- š„ Lesson 10.1 Normal likelihood with variance knownā¢4 minutes
- š„ Lesson 10.2 Normal likelihood with variance unknownā¢3 minutes
- š„ Lesson 11.1 Non-informative priorsā¢8 minutes
- š„ Lesson 11.2 Jeffreys priorā¢3 minutes
- š„ Linear regression in R (Datasets included in Downloads)ā¢17 minutes
- š„ Linear regression in Excel (Analysis ToolPak)ā¢14 minutes
- š„ Linear regression in Excel (StatPlus by AnalystSoft)ā¢14 minutes
- š„ Conclusionā¢1 minute
##### 5 readingsā¢Total 33 minutes
- š Module 4 objectives, assignments, and supplementary materialsā¢3 minutes
- š Supplementary material for Lesson 10ā¢10 minutes
- š Supplementary material for Lesson 11ā¢5 minutes
- š Background for Lesson 12ā¢10 minutes
- š R and Excel code for regressionā¢5 minutes
##### 5 assignmentsā¢Total 63 minutes
- āļø Lesson 9: Demonstrate your knowledgeā¢12 minutes
- āļø Lesson 10: Demonstrate your knowledgeā¢20 minutes
- āļø Lesson 11: Demonstrate your knowledgeā¢10 minutes
- āļø Regression: Demonstrate your knowledgeā¢15 minutes
- āļø Module 4 Honors ā¢6 minutes
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### Instructor
Instructor ratings
## Instructor ratings
We asked all learners to give feedback on our instructors based on the quality of their teaching style.
OK
4\.6
(525 ratings)

[Herbert Lee](https://www.coursera.org/instructor/ucsc)
University of California, Santa Cruz
1 Courseā¢159,482 learners
### Offered by

[University of California, Santa Cruz](https://www.coursera.org/partners/ucsc)
Learn more
## Offered by

[University of California, Santa Cruz](https://www.coursera.org/partners/ucsc)
UC Santa Cruz is an outstanding public research university with a deep commitment to undergraduate education. Itās a place that connects people and programs in unexpected ways while providing unparalleled opportunities for students to learn through hands-on experience.
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## Learner reviews
4\.6
3,227 reviews
- 5 stars
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25\.03%
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5\.23%
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Showing 3 of 3227
D
DG
4
Ā·
Reviewed on Dec 9, 2019
It was a good course for me to get familiar with the new perspective on statistics. Thank you! Maybe, some extended practice exercise at the end of the course would make it even better)
M
MD
4
Ā·
Reviewed on Feb 19, 2020
the notes for the lectures are missing.In my opinion the notes, which includes the video materials could be very useful.the course was good. I learnt some new concepts in bayesian thinking.
M
MM
4
Ā·
Reviewed on Sep 25, 2019
Very clear and informative. Would like a more extensive and combined reference material (PDF, so less need to lookup e.g. definitions of effective sample size for various distributions).
[View more reviews](https://www.coursera.org/learn/bayesian-statistics/reviews)

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## Frequently asked questions
### What are the pre-requisites for this course?
You should have exposure to the concepts from a basic statistics class (for example, probability, the Central Limit Theorem, confidence intervals, linear regression) and calculus (integration and differentiation), but it is not expected that you remember how to do all of these items. The course will provide some overview of the statistical concepts, which should be enough to remind you of the necessary details if you've at least seen the concepts previously. On the calculus side, the lectures will include some use of calculus, so it is important that you understand the concept of an integral as finding the area under a curve, or differentiating to find a maximum, but you will not be required to do any integration or differentiation yourself.
### What computing resources are expected for this course?
Data analysis is done using computer software. This course provides the option of Excel or R. Equivalent content is provided for both options. A very brief introduction to R is provided for people who have never used it before, but this is not meant to be a course on R. Learners using Excel are expected to already have basic familiarity of Excel.
### When will I have access to the lectures and assignments?
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Yes. In select learning programs, you can apply for financial aid or a scholarship if you canāt afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, youāll find a link to apply on the description page.
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| Readable Markdown | This course introduces the Bayesian approach to statistics, starting with the concept of probability and moving to the analysis of data. We will learn about the philosophy of the Bayesian approach as well as how to implement it for common types of data. We will compare the Bayesian approach to the more commonly-taught Frequentist approach, and see some of the benefits of the Bayesian approach. In particular, the Bayesian approach allows for better accounting of uncertainty, results that have more intuitive and interpretable meaning, and more explicit statements of assumptions. This course combines lecture videos, computer demonstrations, readings, exercises, and discussion boards to create an active learning experience. For computing, you have the choice of using Microsoft Excel or the open-source, freely available statistical package R, with equivalent content for both options. The lectures provide some of the basic mathematical development as well as explanations of philosophy and interpretation. Completion of this course will give you an understanding of the concepts of the Bayesian approach, understanding the key differences between Bayesian and Frequentist approaches, and the ability to do basic data analyses. |
| Shard | 97 (laksa) |
| Root Hash | 1995246928644532097 |
| Unparsed URL | org,coursera!www,/learn/bayesian-statistics s443 |