Posterior probability

Posterior probability

• The posterior probability is the probability of parameters $\theta$ given the evidence $X: P(\theta|X)$.
• It contrasts with the likelihood function, which is the probability of the evidence given the parameters $\theta: P(X|\theta)$.
• The two are related as follows：
  $$p(\theta|X) = \frac{P(X|\theta)P(\theta)}{p(X)}$$