Probabilistic Graphical Models: An Introduction

Alexander Denev

Graphical models are a marriage between probability theory and graph theory. They provide a natural tool for dealing with two problems that occur throughout applied mathematics and engineering – uncertainty and complexity – and in particular they are playing an increasingly important role in the design and analysis of machine learning algorithms. Fundamental to the idea of a graphical model is the notion of modularity – a complex system is built by combining simpler parts. Probability theory provides the glue whereby the parts are combined, ensuring that the system as a whole is consistent, and providing ways to interface models to data.

(Jordan 1998)

We argued in the previous chapter that, in our view, a new way of thinking in financial modelling seems necessary. If the reader agrees with us on this point and are convinced by the arguments we have put forward so far, they might want to skip this chapter and continue with the rest of the book, where we shall introduce the new technique, anticipated in the previous chapter, that could overcome some of the issues we have discussed.

In our view, what is needed to solve some of the problems in Chapter 1 is a modelling