A graphical framework for representing the semantics of asymmetric models

Bayesian networks (BNs) are useful for coding conditional independence statements, especially in discrete symmetric models. 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 called the chain event graph (CEG). For symmetric models, all conditional independencies in a BN can be expressed through the topology of a CEG. However, 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. Furthermore, being a function of an ET, the CEG is a more flexible 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 .