In this chapter we look at a number of additional tools that can help in dealing with large or complex Bayesian nets. Again, we are only scratching the surface of a vast topic, and we are guided in our selective choice by our expectations of the problems the typical asset manager is likely to encounter.

Efficient computation

In this section we assume that we have assigned (at least tentatively) all the required conditional probabilities to define the Bayesian net, and that, using the Master Equation, we can therefore obtain the joint probabilities for all the possible values of the nodes. Once we have reached the final leaves and we are about to embark on the optimization we are typically interested only in the joint probabilities of the market risk factors (i.e., the variables associated with the leaves themselves). This requires ‘integrating out’ a large number of variables. Doing so by ‘brute force’ is inefficient. We therefore present a method for variable elimination from Murphy (2001) (a brief tutorial that we warmly recommend, and which we follow closely in the next subsection).

We note in passing that repeated marginalization of variables is also required when we calculate conditional probabilities other than those in the Master Equation. We may want to do so in order to check the reasonableness of the Bayesian net during its construction. See, for instance, the discussion in Chapter 16.