The dynamic chain event graph

Lorna M Barclay,Jim Q Smith,Ann E Nicholson,Peter A Thwaites,Rodrigo A Collazo

doi:10.1214/15-ejs1068

Abstract

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.

Highlights

In this paper we propose a novel class of graphical models called Dynamic Chain Event Graph (DCEG) to model longitudinal discrete processes that exist in many diverse domains such as medicine, biology and sociology
Results such as the one in Theorem 1 allow us to identify particular Extended DCEG subclasses whose models have a strong connection with semi-Markov processes
We have demonstrated here that a dynamic version of the CEG is straightforward to develop and that this class enjoys most of the convenient properties of the CEG

Summary

Introduction

In this paper we propose a novel class of graphical models called Dynamic Chain Event Graph (DCEG) to model longitudinal discrete processes that exist in many diverse domains such as medicine, biology and sociology. These processes often evolve over long periods of time allowing studies to collect repeated multivariate observations at different time points. The CEG concepts presented here are a natural extension of those in Smith and Anderson (2008); Thwaites et al (2010); Freeman and Smith (2011a) These conceptual adaptations will allow us to directly use these concepts to define a DCEG model.

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Conclusion