Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science, 2nd Edition

2.2 Reasoning with Bayesian networks and influence diagrams

In this chapter, the ‘black box’ of the computational architecture of Bayesian networks is examined and it is shown that the architecture works according to the principles of the logic of uncertainty that we have outlined in Chapter 1. Formal proofs are not given of the mathematical results exploited because, for readers interested in practical applications of Bayesian networks and who are going to use commercial software already available, it is more important to understand why the answers provided bythe ‘black box’ can be trusted, rather than to know in any detail the mathematics of the inference engine.

Example 2.4

(‘Jack loved Lulu’, continued) In order to be able to apply Bayes' rule in the ‘Lulu’ case, it is necessary to calculate the marginal distributions of the evidence nodes E and W from the conditional probabilities in (2.2). Consider, first, the task of computing the marginal probability distribution of E:

2.3

The marginal probability distribution of C is given by

2.4

The variable B is d-separated from given , therefore we can rewrite (2.4) as

2.5

The final goal is the marginal probability distribution ...