The causal manipulation and Bayesian estimation of chain event graphs

Discrete Bayesian Networks (BNs) have been very successful as\ud a framework both for inference and for expressing certain causal hypotheses. In this paper we present a class of graphical models called\ud the chain event graph (CEG) models, that generalises the class of discrete BN models. This class is suited for representing conditional independence and sample space structures of asymmetric models. It retains many useful properties of discrete BNs, in particular admitting\ud conjugate estimation. It provides a flexible and expressive framework\ud for representing and analysing the implications of causal hypotheses,\ud expressed in terms of the effects of a manipulation of the generating\ud underlying system.We prove that, as for a BN, identifiability analyses\ud of causal effects can be performed through examining the topology\ud of the CEG graph, leading to theorems analogous to the Backdoor\ud theorem for the BN.