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Paper No. 06-08

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PE Anderson and JQ Smith

Bayesian Representations Using Chain Event Graphs

Abstract: Bayesian networks (BNs) are useful for coding conditional independence statements between a given set of measurement variables. On the other hand, event trees (ETs) are convenient for representing asymmetric structure and how situations unfold. In this paper we report the development of a new graphical framework for discrete probability models called the Chain Event Graph (CEG). The class of CEG models contains finite BNs as a special case. Unlike the BN, the CEG is equally appropriate for representing conditional independencies in asymmetric systems and does not need dependent variables to be specified in advance. As with the BN, it also provides a framework for learning relevant conditional probabilities and propagation. Furthermore, being a function of an ET, the CEG is a more exible way of representing various causal hypotheses than the BN. This new framework is illustrated throughout by a biological regulatory network: the tryptophan metabolic pathway in the bacterium E. coli.