An N Time-Slice Dynamic Chain Event Graph

Abstract

The Dynamic Chain Event Graph (DCEG) is able to depict many classes of discrete random processes exhibiting asymmetries in their developments and context-specific conditional probabilities structures. However, paradoxically, this very generality has so far frustrated its wide application. So in this paper we develop an object-oriented method to fully analyse a particularly useful and feasibly implementable new subclass of these graphical models called the N Time-Slice DCEG (NT-DCEG). After demonstrating a close relationship between an NT-DCEG and a specific class of Markov processes, we discuss how graphical modellers can exploit this connection to gain a deep understanding of their processes. We also show how to read from the topology of this graph context-specific independence statements that can then be checked by domain experts. Our methods are illustrated throughout using examples of dynamic multivariate processes describing inmate radicalisation in a prison.

Properties of an N Time-Slice Dynamic Chain Event Graph

“…Example 1. We revisit the example in [21] that summarily describe the radicalisation dynamic of inmates in a prision using three random variables:…”

“…A DCEG model [21] provides a compact colourful representation of a probabilistic tree through three simple steps: the elicitation of an event tree, its transformation into a staged tree and finally its wrapping into a DCEG graph. Using colours and some graphical transformations, this framework combines the graphical expressiveness of DBNs with the flexibility of tree graphs to depict both context-specific information and asymmetric developments.…”

“…In [21] we develop a method for depicting an infinite event tree using a set of objects, each of whom encapsulates a finite event corresponding to a finite process. The objects are concatenated according some domain-based rules.…”

“…Since its paths can be used to depict the various possible sequences of events a unit can experience over time, a tree provides a modeller with a flexible framework to accommodate asymmetric developments and context-specific structures. The Dynamic Chain Event Graph (DCEG) [20,21] is a particular type of infinite tree-based graphical model developed for discrete longitudinal data. Build upon a Chain Event Graph (CEGs) [22] a DCEG [20] was originally envisaged to elicit simple semi-Markov processes defined as a very small number of discrete states.…”

“…Recall that a CEG is supported by a finite tree and so appropriate to construct models in a non-dynamic context. In [21] we rigorously advanced the foundation of DCEGs for specific classes of Markov process and defined a promising subclass called N Time-Slice DCEG (NT-DCEG). Using objects and a special family of CEGs, we then presented a methodology to construct an NT-DCEG and to reason with it.…”