Chain event graph map model selection

When looking for general structure from a finite discrete data set one can search over the class of Bayesian Networks (BNs). The class of Chain Event Graph (CEG) models is however much more expressive and is particularly suited to depicting hypotheses about how situations might unfold. Like the BN, the CEG admits conjugate learning on its conditional probability parameters using product Dirichlet priors. The Bayes Factors associated with different CEG models can therefore be calculated in an explicit closed form, which means that search for the maximum a posteriori (MAP) model in this class can be enacted by evaluating the score function of successive models and optimizing. Local search algorithms can be devised for the class of candidate models, but in this paper we concentrate on the process of scoring the members of this class