Notes on Bayesian Networks

A Bayesian network (from now on BN) of a set of variables X = {X1, . . . , Xn} represents a joint probability distribution over those variables. It consists of a network structure that encodes assertions of conditional independence in the distribution and a set of conditional probability distributions corresponding to that structure. It is graphically represented by directed acyclic graphs, whose nodes denotes the random variables, which may be observable quantities, latent variables, unknown parameters or hypotheses. Edges represent conditional dependencies, so that nodes which are disconnected represent variables which are conditionally independent of each other.