The Lorax Problem: Introduction to Bayesian Networks

Abstract

The “Lorax Problem” introduces Bayesian networks, another set of methods that makes use of Bayes’ Theorem. The ideas are first explained in terms of a small, standard example that explores two alternative hypotheses for why the grass is wet: the sprinkler is on versus it is raining. The chapter describes how to depict causal models graphically with the use of influence diagrams and directed acyclic graphs. Bayes’ Theorem is used to compute conditional probabilities and to update probabilities once new information is obtained or assumed. The software program Netica is introduced. Finally, the chapter provides a second example of Bayesian networks based on The Lorax by Dr. Seuss. The reader will gain a firm understanding of parent nodes (also known as root nodes), child nodes, conditional probability tables (CPTs), and the chain rule for joint probability.