Bayesian Statistics in simple English
읽은 글은 Bayesian Statistics explained to Beginners in Simple English
baysian inference가 뭔가 찾아보다가 발견한 문서.(variational inference와는 어떻게 다른거지?)
1. Frequentist Statistics
2. The Inherent Flaws in Frequentist Statistics
여기 p-value랑 C.I.(confidence interval)나오는데, 이런 기본용어 설명이 여기가 기가 막히다. 이것도 따로 빼둔다.
3. Bayesian Statistics
3.1 Conditional Probability
Bayes theorem is built on top of conditional probability and lies in the heart of Bayesian Inference.
3.2 Bayes Theorem
\(\Large P(A|B) = \frac{\Large P(B|A_i) P(A_i) }{\Large \sum_{i=1}^n P(B|A_i)P(A_i)} \)
4. Bayesian Inference
prior × liklihood = posterior × evidence
cf. Variational Inference (pdf)
4.1. Bernoulli likelihood function
\(\Large P(y|θ)=θ^y(1-θ)^{1-y}\)
\( y =\{0, 1\}, θ = (0, 1) \)
\(y=1\) means 'head of a coin', \(θ\) means fairness of a coin.
so,
$$ P(y_1, y_2, ... , y_n | θ) = \prod_1^n P(y_i|θ) $$ $$ P(z,N|θ) = θ^z (1-θ)^{N-z} $$ where z is a number of heads and N is a number of flips.