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.