Rule of Probabilities

• chain rule
• sum rule: $p(X)={\sum }_{Y}p(X,Y)$
• product rule: $p(X,Y)=p(Y\mid X)p(X)$
• relation with Bayes theorem

$$p(Y\mid X)=\frac{p(X\mid Y)p(Y)}{p(X)}$$

Evidence 는 다음과 같이 sum 과 product rule 을 동시에 사용하여 계산한다.

$$p(X)=\sum _{Y}p(X\mid Y)p(Y)$$

B) Related

C) References