Modelling with Non-stratified Chain Event Graphs

Abstract

Chain Event Graphs (CEGs) are a recent probabilistic graphical modelling tool that have proved successful in modelling scenarios with context-specific independencies. Although the theory underlying CEGs supports appropriate representation of structural zeroes, the literature so far does not provide an adaptation of the vanilla CEG methods for a real-world application presenting structural zeroes also known as the non-stratified CEG class. To illustrate these methods, we present a non-stratified CEG representing a public health intervention designed to reduce the risk and rate of falling in the elderly. We then compare the CEG model to the more conventional Bayesian Network model when applied to this setting.

Constructing a Chain Event Graph from a Staged Tree

“…The fifth dataset is from the Christchurch Health and Development Study (CHDS) conducted at the University of Otago, New Zealand (see Fergusson et al (1986)) and the last two are simulated datasets which have structural zeros. It has been shown that the last three datasets also exhibit context-specific conditional independences (Collazo et al, 2018;Shenvi et al, 2018;Shenvi and Smith, 2019). Table 1 2 gives for each dataset the number of situations in the staged tree output by the AHC algorithm (|S (S)|), the maximum depth of the staged tree (m) and the time taken (in milliseconds) by the two compacting algorithms (T Baseline and T Optimal ) as well as the number of positions in the resulting CEG found by the two algorithms ( V(C Baseline) and V(C Optimal) ).…”

“…Non-stratified CEGs provide a truer representation of a wide range of processes containing structural zeroes (see e.g. Shenvi et al (2018); Shenvi and Smith (2019)).…”

“…Although the size of an event tree increases linearly with the number of events involved in the evolution of the process and this may become unwieldy for large complex processes, they are nonetheless easy for the statistician to transparently elicit from the natural language descriptions of a domain expert. Embedding structural zeros within an event tree is a matter of simply not drawing the corresponding branch in the tree (Shenvi et al, 2018). However, a more compact representation of an event tree while retaining its properties and transparency is desirable.…”

“…In particular, the advantages of the CEG over a BN can be demonstrated (Barclay et al, 2013;Silander and Leong, 2013). However, we are increasingly finding many applications both in forensic science and in public health where the CEG representation is not stratified (Shenvi et al, 2018;Collazo et al, 2018). So it is timely that automatic algorithms are available to make this transformation for any staged tree.…”

Bayesian Model Averaging of Chain Event Graphs for Robust Explanatory Modelling

“…Here, we have a non-stratified CEG example based on simulated falls data for 1000 individuals aged over 65. Although simulated, this data was carefully constructed to be calibrated to the various studies of falls in the elderly [Shenvi et al, 2018].…”