常用到的概率公式

1.贝叶斯公式

 \begin{equation} P(A|B)=\frac{P(A,B)}{P(B)}=\frac{P(B|A)P(A)}{P(B)} \end{equation}

2.Chain Rule

 \begin{equation} P(x_{1}, x_{2}, ... , x_{n}) = P(x_{1})P(x_{2}|x_{1}) P(x_{3}|x_{1}^2) ... P(x_{n}|x_{1}^{n-1}) \end{equation}

其中$x_{1}^{n-1} = x_{1},x_{2}, ... , x_{n-1}$

变种：

 \begin{equation}  P(A,B|C) = P(A|C)P(B|A,C) \end{equation}