Bayesian Networks

Abstract

This chapter deals with Bayesian networks. The term usually refers to graphical models (most often with discrete variables) based on directed acyclic graphs (DAGs), applied in the expert system context. The emphasis differs somewhat from ordinary statistical modeling, since the DAG is usually taken as known and the focus is on efficient calculation of conditional probabilities of states of unobserved variables. Implemented naively, these calculations would be forbiddingly complex, but using message passing techniques they can be implemented very efficiently. (Somewhat confusingly, Bayesian networks are not in fact very Bayesian, in the sense that the Bayesian inferential methods are not normally used.) We explain the techniques and illustrate them on an example involving chest clinic data, using the package gRain. We show how appropriate R objects can be created, compiled and probability propagation performed in order to compute the required quantities. Topics covered in later sections include simulation and prediction using the network objects, use of the RHugin package, and structural learning, i.e., how the network may be learnt from the data.