A Separation Theorem for Chain Event Graphs
This provides a tool for analysts working with complex statistical models where BNs are insufficient, though it is incremental as it extends existing concepts to a specific graph type.
The paper tackles the problem that Bayesian Networks (BNs) cannot fully depict dependence structures for many statistical problems, by introducing a separation theorem for Chain Event Graphs (CEGs) that allows analysts to identify conditional independence statements from the graph topology, analogous to the d-separation theorem for BNs.
Bayesian Networks (BNs) are popular graphical models for the representation of statistical problems embodying dependence relationships between a number of variables. Much of this popularity is due to the d-separation theorem of Pearl and Lauritzen, which allows an analyst to identify the conditional independence statements that a model of the problem embodies using only the topology of the graph. However for many problems the complete model dependence structure cannot be depicted by a BN. The Chain Event Graph (CEG) was introduced for these types of problem. In this paper we introduce a separation theorem for CEGs, analogous to the d-separation theorem for BNs, which likewise allows an analyst to identify the conditional independence structure of their model from the topology of the graph.