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| Meta Title | 最大似然估计(MLE)原理及计算方法-腾讯云开发者社区-腾讯云 |
| Meta Description | 1)有两堆球,其中A堆有99个白球和1个黑球,B堆有99个黑球和1个白球。假如随便摸一个球,发现是黑球,那么这个球更有可能来自于哪一堆? |
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| Boilerpipe Text | 1. 实际例子 1)有两堆球,其中A堆有99个白球和1个黑球,B堆有99个黑球和1个白球。假如随便摸一个球,发现是黑球,那么这个球更有可能来自于哪一堆? 2)猎人和徒弟去打猎,打倒了一只兔子,更可能是谁打中的? 3)一堆球,里边有黑白两色的球,其中一种颜色的有90个,另一种颜色的有10个。如果摸出一个球是黑色的,那么里边哪种颜色有90个? 第一个肯定觉得是来自B堆,第二个中更可能是师傅,第三个里边黑球有90个。我们的估计基于,概率最高的事情,更可能发生。一次实验就出现的事件,这件事有较大的概率发生。 2. 数学表述 最大似然估计这个名字是由高斯先提出,Fisher后来重新提出并证明了一些特征。这是统计学中的常用方法,机器学习中的逻辑回归中也是基于它计算的损失函数。 当样本分布是离散型: 当样本分布为连续型时: 一般情况下求估计值的步骤:
1)构造似然函数?(?)
2)取对数:???(?) 似然函数是连乘,不好求导;取对数后可化为加法,求导方便。
3)求导,计算极值
4)解方程,得到? 如果似然方程无解,或者似然函数不可导,则需要考虑其他方法。 3. 计算实例 (此题来自于 https://wenku.baidu.com/view/0d9af6aa172ded630b1cb69a.html )
参考:
1) https://wenku.baidu.com/view/0d9af6aa172ded630b1cb69a.html
2) https://medium.com/@rrfd/what-is-maximum-likelihood-estimation-examples-in-python-791153818030 、 |
| Markdown | [生信编程日常](https://cloud.tencent.com/developer/user/7144248)
## 最大似然估计(MLE)原理及计算方法
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[社区首页](https://cloud.tencent.com/developer) \>[专栏](https://cloud.tencent.com/developer/column) \>最大似然估计(MLE)原理及计算方法
# 最大似然估计(MLE)原理及计算方法

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发布于 2020-06-05 11:04:30
发布于 2020-06-05 11:04:30
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文章被收录于专栏:[生物信息学、python、R、linux](https://cloud.tencent.com/developer/column/85939)[生物信息学、python、R、linux]()
###### 1\. 实际例子
1)有两堆球,其中A堆有99个白球和1个黑球,B堆有99个黑球和1个白球。假如随便摸一个球,发现是黑球,那么这个球更有可能来自于哪一堆?
2)猎人和徒弟去打猎,打倒了一只兔子,更可能是谁打中的?
3)一堆球,里边有黑白两色的球,其中一种颜色的有90个,另一种颜色的有10个。如果摸出一个球是黑色的,那么里边哪种颜色有90个?
第一个肯定觉得是来自B堆,第二个中更可能是师傅,第三个里边黑球有90个。我们的估计基于,概率最高的事情,更可能发生。一次实验就出现的事件,这件事有较大的概率发生。
###### 2\. 数学表述
最大似然估计这个名字是由高斯先提出,Fisher后来重新提出并证明了一些特征。这是统计学中的常用方法,机器学习中的逻辑回归中也是基于它计算的损失函数。
当样本分布是离散型:

当样本分布为连续型时:

一般情况下求估计值的步骤: 1)构造似然函数?(?) 2)取对数:???(?) 似然函数是连乘,不好求导;取对数后可化为加法,求导方便。 3)求导,计算极值 4)解方程,得到?
如果似然方程无解,或者似然函数不可导,则需要考虑其他方法。
###### 3\. 计算实例
(此题来自于[https://wenku.baidu.com/view/0d9af6aa172ded630b1cb69a.html](https://cloud.tencent.com/developer/tools/blog-entry?target=https%3A%2F%2Flinks.jianshu.com%2Fgo%3Fto%3Dhttps%253A%252F%252Fwenku.baidu.com%252Fview%252F0d9af6aa172ded630b1cb69a.html&objectId=1639197&objectType=1&contentType=undefined))



参考: 1)[https://wenku.baidu.com/view/0d9af6aa172ded630b1cb69a.html](https://cloud.tencent.com/developer/tools/blog-entry?target=https%3A%2F%2Flinks.jianshu.com%2Fgo%3Fto%3Dhttps%253A%252F%252Fwenku.baidu.com%252Fview%252F0d9af6aa172ded630b1cb69a.html&objectId=1639197&objectType=1&contentType=undefined) 2)[https://medium.com/@rrfd/what-is-maximum-likelihood-estimation-examples-in-python-791153818030](https://cloud.tencent.com/developer/tools/blog-entry?target=https%3A%2F%2Flinks.jianshu.com%2Fgo%3Fto%3Dhttps%253A%252F%252Fmedium.com%252F%2540rrfd%252Fwhat-is-maximum-likelihood-estimation-examples-in-python-791153818030&objectId=1639197&objectType=1&contentType=undefined)
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- 2\. 数学表述
- 3\. 计算实例
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