Properties of an N Time-Slice Dynamic Chain Event Graph

TL;DR

This paper explores properties of N Time-Slice Dynamic Chain Event Graphs (NT-DCEGs), showing their relation to Dynamic Bayesian Networks, methods for construction, and applications in modeling complex dynamic processes.

Contribution

It introduces the class of NT-DCEGs, proves their relation to Bayesian networks, and develops a construction method and interpretative tools for dynamic process modeling.

Findings

NT-DCEGs include all discrete N time-slice Dynamic Bayesian Networks.

A distributive construction method for NT-DCEGs is developed.

NT-DCEGs can depict structural and causal hypotheses in dynamic processes.

Abstract

A Dynamic Chain Event Graph (DCEG) provides a rich tree-based framework for modelling a dynamic process with highly asymmetric developments. An N Time-Slice DCEG (NT-DCEG) is a useful subclass of the DCEG class that exhibits a specific type of periodicity in its supporting tree graph and embodies a time-homogeneity assumption. Here some desired properties of an NT-DCEG is explored. In particular, we prove that the class of NT-DCEGs contains all discrete N time-slice Dynamic Bayesian Networks as special cases. We also develop a method to distributively construct an NT-DCEG model. By exploiting the topology of an NT-DCEG graph, we show how to construct intrinsic random variables which exhibit context-specific independences that can then be checked by domain experts. We also show how an NT-DCEG can be used to depict various structural and Granger causal hypotheses about a given process. Our methods are illustrated throughout using examples of dynamic multivariate processes describing inmate radicalisation in a prison.