Bayesian Graphical Models

Mathematically, a Bayesian graphical model is a representation of the joint probability distribution for a set of variables. The most frequently used type of Bayesian graphical models are Bayesian networks, but other types exist and Bayesian networks can be seen as a special type of Chain Graphs. The structural part of a Bayesian graphical model is a graph consisting of nodes and edges. The nodes represent variables. The set of all variables, called the universe, is denoted U. A variable may be discrete or continuous. For the sake of simplicity this article focuses on models with only discrete variables, and refers to the variable values as states. An edge between two nodes A and B indicates a direct influence between the state of A and the state of B.

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