Graphical Modelling

Marcel van Oijen

Chapter Chapter 16 in Bayesian Compendium, 2024, pp 119-133 from Springer

Abstract: Abstract A graphical model (GM), also called a probabilistic network, is a representation of a joint probability distribution. A GM has two parts: (1) a graph with nodes connected by edges and (2) information about the nodes. So the graph is just the visible part of the model. GMs do not represent a new kind of statistical model; they are just helpful tools for analysing joint probability distributions. Every distribution can be represented by a GM, so whatever your research problem or modelling method is, you can choose to use a GM to organise your thinking. And you can choose from multiple kinds of GM as we show in Fig. 16.1. The two most prominent types are Bayesian networks (BN, which use directed graphs so that the edges are arrows) and Markov Random Fields (MRF, which use undirected graphs) (Briganti et al., Psychol Methods 28:947–961, 2023). Both classes can represent continuous as well as discrete probability distributions. The different types of GM all come with their own apparatus for designing, interpreting and updating the distributions that they represent. The graphs play an important role in that they indicate ways of decomposing the distribution into conditionally independent parts. Bayesian calibration of a GM consists of acquiring data for one or more nodes (the others remain unobserved latent variables) and using Bayes’ Theorem to update the joint probability distribution. We leave this very short general introduction to GM here to concentrate on Gaussian Bayesian Networks (GBNs), which can showcase most of the advantages that GM bring. But we shall finish this chapter with some general comments on GM.

Date: 2024
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DOI: 10.1007/978-3-031-66085-6_16

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