Bayesian Model Averaging of Chain Event Graphs for Robust Explanatory Modelling
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Chain Event Graphs (CEGs) are a widely applicable class of probabilistic graphical models that are able to represent context-specific independence statements and asymmetric unfoldings of events in an easily interpretable way. Existing model selection literature on CEGs has focused on obtaining the maximum a posteriori (MAP) CEG. However, MAP selection is well-known to ignore model uncertainty. Here, we explore the use of model averaging over this class. We demonstrate that such methods express model uncertainty and lead to more robust inference. Because the space of possible CEGs is huge, scoring models exhaustively for model averaging in all but small problems is prohibitive. However we show that a bespoke class of hybrid forward sampling and greedy search algorithms can successfully and intelligently traverse this space of candidate models. By applying a simple version of our search method to two known case studies, we can illustrate the efficacy of such methods compared to more standard MAP modelling. We also demonstrate how its outputs systematically inform those component hypotheses that are most robustly supported the data and high-scoring alternative models to the MAP model.
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