## ABSTRACT

We have now seen how Bayes' theorem enables us to correctly update a prior probability for some unknown event when we see evidence about the event. But in any real-world risk assessment problem there will be many unknown events and many different pieces of evidence, some of which may be related. We already saw in Chapter 3 examples of such risk assessment problems. When we represent such problems graphically (with all uncertain variables being represented as nodes and an edge between two nodes representing a relationship) we have a Bayesian Network (BN). It turns out that Bayes' theorem can be applied to correctly update evidence in these more general complex problems, and the purpose of this chapter is to explain exactly how this is done and under what constraints.