Bayesian Inference

Statistics micro

The very basic case

We start from a very basic case, suppose we know $B$ already happens, the probability of $A$ happens is:

$$P(A|B)=\frac{P(A\cap B)}{P(B)}$$

The Bayes Rule

Thus we know:

$$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$$

• $P(A|B)$ is posterior （后验概率）