Zzong's Notes

product rule

1 min read

Product Rule

  • : marginal distribution of the first random variable
  • : conditional distribution of second random variable given first

해석

  • The product rule can be interpreted as the fact that every joint distribution of two random variables can be factorized (or product) of two other distributions.

Related

References

링크된 언급

3
Bayes theorem

...하기 위해 단순히 chain rule (probability) 을 사용할 수 있다. C) Some Notes P(B\mid A)P(A)=P(A,B)=P(A\mid B)P(B) 인 이유: product rule D) Related E) References

posterior predictive distribution

...의 식에서 \mathbf{x} 가 사라진 이유는, 관측되지 않은 데이터와 기존 데이터는 독립이라는 가정이 있기 때문이다. 첫번째 식에서 두번째 식으로 유도되는 이유는 sum rule 과 product rule 을 활용했기 때문 2. 예시 from stackoverflow \begin{aligned}p(x\mid\mathcal{D})&\stackrel{(a)}{=}\int {0}^{1}...

sum rule

...rd, in the sense that there is no known polynomial time algorithm to calculate them exactly. 3. Related product rule, marginal distribution 4. References