What is Bayes’ Rule?

Bayes’ Rule is based on the definition of conditional probability and allows the original probability statement to be reversed and conditioned on the other event. For two events A and B, Bayes’ Rule is given by:

This formulation is useful in cases where the joint probability of A and B occurring is difficult to compute, but the conditional and marginal distributions are available. Bayes’ Rule forms the foundation for Bayesian inference, which treats the parameters of a model as random variables, where inference incorporates information from both the data observed and a prior belief about how the parameters might behave.