Born at the intersection of artificial intelligence, statistics, and probability, Bayesian networks (Pearl, 1988) are a representation formalism at the cutting edge of knowledge discovery and data mining (Heckerman, 1997). Bayesian networks belong to a more general class of models called probabilistic graphical models (Whittaker, 1990; Lauritzen, 1996) that arise from the combination of graph theory and probability theory, and their success rests on their ability to handle complex probabilistic models by decomposing them into smaller, amenable components. A probabilistic graphical model is defined by a graph, where nodes represent stochastic variables and arcs represent dependencies among such variables. These arcs are annotated by probability distribution shaping the interaction between the linked variables. A probabilistic graphical model is called a Bayesian network, when the graph connecting its variables is a directed acyclic graph (DAG). This graph represents conditional independence assumptions that are used to factorize the joint probability distribution of the network variables, thus making the process of learning from a large database amenable to computations. A Bayesian network induced from data can be used to investigate distant relationships between variables, as well as making prediction and explanation, by computing the conditional probability distribution of one variable, given the values of some others.
A Bayesian network is a graph, where nodes represent stochastic variables and (arrowhead) arcs represent dependencies among these variables. In the simplest case, variables are discrete, and each variable can take a finite set of values.