PA Thwaites and JQ Smith
Separation Theorems for Chain Event Graphs
Abstract: A separation theorem on a graphical model allows an analyst to identify the conditional independence statements it logically entails using only topology of the graph. In this paper we prove separation theorems associated with a new coloured graphical model called a Chain Event Graph (CEG). The class of CEG models generalises the class of finite discrete Bayesian Network models. Here we formally define this model class, and consider the set of permissible conditional independence queries on this graph. We provide necessary and sufficient conditions for these conditional independence statements to hold on a subclass of uncoloured CEGs called simple CEGs. We then prove sufficient conditions for such statements to hold on a much larger subclass called regular CEGs. The paper is illustrated with a running example demonstrating the application of these theorems.