《模式识别与机器学习》学习笔记：2.1 二值变量

术语

术语	中文含义	备注
Bernoulli distribution		p69
sufficient statistic		*, p69
sample mean		p70
binomail distribution		p70
conjugacy		p71页第一次出现
beta distribution		p71
gamma function		p71
hyperparameter		#, p71
effective number of observations		#, p72
sequential approach		*, p73

注：#(不确定含义)，*(重点)

2.1 Binary Varibles

P70, an extreme example of the over-fitting associated with maximum likelihood. And we can arrive at more sensible conclusions through the introduction of a prior distribution.

70页举例说明了极大似然的过拟合现象，提出可以通过引入先验分布获得更合理的结论。

2.1.1 The beta distribution

二值分布的先验分布：β分布

 

The posterior distribution, which is proportional to the product of the prior and the likelihood function, have the same functional form as the prior. This property is called conjugacy.

如果后验分布与先验分布和似然函数的乘积成比例，且与先验分布有着相同的函数形式。我们称这种性质为共轭。

 

Figure 2.2 and 2.3; Formula 2.21 and 2.24

图的解说和公式含义

 

公式2.24中，先验分布方差和后验分布方差的关系。

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作者：兔纸张   来源：博客园 ( http://www.cnblogs.com/geiliCode )