Prior Probability

Posterior Probability

Posterior probability is a type of conditional probability in Bayesian statistics.

A posterior probability distribution is a conditional probability distribution obtained by applying the distributional form of Bayes’ Theorem.

Given a prior belief that a probability distribution function is {\displaystyle p(\theta )}p(\theta ) and that the observations {\displaystyle x}x have a likelihood {\displaystyle p(x|\theta )}p(x|\theta ), then the posterior probability is defined as

where is the normalizing constant and is calculated as

for continuous , or by summing over all possible values of for discrete .