Properties of an N Time-Slice Dynamic Chain Event Graph
This work provides a theoretical framework for modeling complex dynamic processes like inmate radicalization, but it appears incremental as it builds on existing DCEG concepts with specific periodicity assumptions.
The paper tackles the modeling of dynamic processes with asymmetric developments by exploring properties of an N Time-Slice Dynamic Chain Event Graph (NT-DCEG), proving it contains all discrete N time-slice Dynamic Bayesian Networks as special cases and developing methods for distributive construction and causal hypothesis depiction.
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.