Peter A. Thwaites

Causal analysis with Chain Event Graphs

As the Chain Event Graph (CEG) has a topology which represents sets of conditional independence statements, it becomes especially useful when problems lie naturally in a discrete asymmetric non-product space domain, or when much context-specific information is present. In this paper we show that it can also be a powerful representational tool for a wide variety of causal hypotheses in such domains. Furthermore, we demonstrate that, as with Causal Bayesian Networks (CBNs), the identifiability of the effects of causal manipulations when observations of the system are incomplete can be verified simply by reference to the topology of the CEG. We close the paper with a proof of a Back Door Theorem for CEGs, analogous to Pearls Back Door Theorem for CBNs.

The Dynamic Chain Event Graph

In this paper we develop a formal dynamic version of Chain Event Graphs (CEGs), a particularly expressive family of discrete graphical models. We demonstrate how this class links to semi-Markov models and provides a convenient generalization of the Dynamic Bayesian Network (DBN). In particular we develop a repeating time-slice Dynamic CEG providing a useful and simpler model in this family. We demonstrate how the Dynamic CEG’s graphical formulation exhibits asymmetric conditional independence statements and also how each model can be estimated in a closed form enabling fast model search over the class. The expressive power of this model class together with its estimation is illustrated throughout by a variety of examples that include the risk of childhood hospitalization and the efficacy of a flu vaccine.

A New Method for tackling Asymmetric Decision Problems

Chain Event Graphs are probabilistic graphical models designed especially for the analysis of discrete statistical problems which do not admit a natural product space structure. We show here how they can be used for decision analysis through designation of some nodes as decision nodes, and the addition of utilities. We provide a local propagation algorithm for finding an optimal decision strategy and maximising expected utility. We also compare CEGs with Influence diagrams, Valuation Networks, Sequential decision diagrams, Sequential influence diagrams and Decision circuits for the representation and analysis of asymmetric decision problems.

A graphical method for simplifying Bayesian games

If the influence diagram (ID) depicting a Bayesian game is common knowledge to its players then additional assumptions may allow the players to make use of its embodied irrelevance statements. They can then use these to discover a simpler game which still embodies both their optimal decision policies. However the impact of this result has been rather limited because many common Bayesian games do not exhibit sufficient symmetry to be fully and efficiently represented by an ID. The tree-based chain event graph (CEG) has been developed specifically for such asymmetric problems. By using these graphs rational players can make analogous deductions, assuming the topology of the CEG as common knowledge. In this paper we describe these powerful new techniques and illustrate them through an example modelling a game played between a government department and the provider of a website designed to radicalise vulnerable people.