Bayesian MAP Model Selection of Chain Event Graphs

TL;DR

This paper introduces a Bayesian MAP model selection method for chain event graphs, extending Bayesian network techniques to better handle asymmetric and ordered event spaces with complete sampling.

Contribution

It develops a conjugate closed-form model selection approach for chain event graphs using product Dirichlet priors and proves homogeneity conditions for these priors.

Findings

Closed-form Bayesian MAP model selection is feasible for chain event graphs.

Homogeneity assumptions characterize the product Dirichlet prior in this context.

Demonstrated techniques on educational examples.

Abstract

The class of chain event graph models is a generalisation of the class of discrete Bayesian networks, retaining most of the structural advantages of the Bayesian network for model interrogation, propagation and learning, while more naturally encoding asymmetric state spaces and the order in which events happen. In this paper we demonstrate how with complete sampling, conjugate closed form model selection based on product Dirichlet priors is possible, and prove that suitable homogeneity assumptions characterise the product Dirichlet prior on this class of models. We demonstrate our techniques using two educational examples.