Chapter 5 - Foundations of Bayesian Networks

Abstract

This chapter introduces Bayesian networks and inference in Bayesian networks. Bayes’ theorem was developed in the eighteenth century. Since that time the theorem has had a great impact on statistical inference because it enables the inference of the probability of a cause when its effect is observed. Gradually, the method was extended to model the probabilistic relationships among many causally related variables. The graphical structures that describe these relationships have come to be known as Bayesian networks. This chapter defines Bayesian networks and discusses their properties. The methods of representation of Bayesian networks are also discussed and causal networks are defined as Bayesian networks. Following this, the study demonstrates how causal graphs often yield Bayesian networks. Under this, it explains the concept of causality, taking into account the operational definition of a cause, manipulation, causal relationships, and Merck's manipulation study. It also discusses the method of doing probabilistic inference using Bayesian networks. Furthermore, it deals with Bayesian networks containing continuous variables. Finally, it explores the question of the method of obtaining probability, demonstrating two techniques, in which the first technique concerns the case where a node has multiple parents and the second technique concerns nodes that represent continuous random variables.