A New Family of Non-Local Priors for Chain Event Graph Model Selection

Abstract

Chain Event Graphs (CEGs) are a rich and provenly useful class of graphical models. The class contains discrete Bayesian Networks as a special case and is able to depict directly the asymmetric context-specific statements in the model. But bespoke efficient algorithms now need to be developed to search the enormous CEG model space. In different contexts Bayes Factor scored search algorithm using non-local priors (NLPs) has recently proved very successful for searching other huge model spaces. Here we define and explore three different types of NLP that we customise to search CEG spaces. We demonstrate how one of these candidate NLPs provides a framework for search which is both robust and computationally efficient. It also avoids selecting an overfitting model as the standard conjugate methods sometimes do. We illustrate the efficacy of our methods with two examples. First we analyse a previously well-studied 5-year longitudinal study of childhood hospitalisation. The second much larger example selects between competing models of prisoners’ radicalisation in British prisons: because of its size an application beyond the scope of earlier Bayes Factor search algorithms.