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Methodological advances in explainable modelling using chain event graphs
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Strong, Peter (2023) Methodological advances in explainable modelling using chain event graphs. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b394964
Abstract
Chain Event Graphs (CEGs) are an easily interpretable, versatile class of probabilistic graphical models that represent context-specific relationships and asymmetric event unfoldings. As an asymmetric extension of discrete Bayesian networks, CEGs provide a compact illustration of detailed dependence structures through the use of colour and by modifying the graphs topology. Although other model selection methods have been studied, CEG model selection literature has primarily focused on obtaining the maximum a posteriori (MAP) CEG. However, this method ignores model uncertainty and therefore the uncertainty of their contained independence statements. We propose using Bayesian model averaging (BMA) to quantify model uncertainty, leading to more robust inference by comparing features across high-scoring models. We provide a simple modification of an existing model selection algorithm, that samples the model space, to illustrate the efficacy of Bayesian model averaging compared to more standard MAP modelling. Recent improvements in structure learning have not mitigated the computational complexity involved in modelling larger applications. They either: fail to scale efficiently when the number of events considered increases; do not find comparable models to existing methods or a priori restrict the model space. We propose an alternative algorithm, using a totally-ordered hyperstage, to obtain a quadratically scaling structural learning algorithm for staged trees, restricting the model space a-posteriori. Our approach outperforms existing methods in computational time, whilst providing comparable model scores. This enables learning more complex relationships than existing model selection techniques by expanding the model space. We consider how CEGs can improve the explainability of Agent-Based Models (ABMs), a popular model class in social science, by providing a Bayesian framework. Although ABMs lack the methods to embed more principled strategies of performing inference to estimate and validate the models, CEGs can fill this gap by accurately representing ABMs. Using a CEG, we illustrate transforming an elicited ABM into a Bayesian framework and outline the benefits of this approach.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Graph theory, Bayesian statistical decision theory, Mathematical statistics -- Graphic methods, Trees (Graph theory), Multiagent systems | ||||
Official Date: | April 2023 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Smith, J. Q., 1953- | ||||
Sponsors: | Engineering and Physical Sciences Research Council ; Medical Research Council (Great Britain) | ||||
Format of File: | |||||
Extent: | xvii, 136 pages : illustrations | ||||
Language: | eng |
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