  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.
