Shenvi, Aditi (2021) Non-stratified chain event graphs : dynamic variants, inference and applications. PhD thesis, University of Warwick.

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Abstract

A chain event graph (CEG) is a graphical model that is constructed by identifying the probabilistic symmetries within the tree-based description of a process. CEGs generalise Bayesian networks (BNs) by representing context-specific conditional independencies within their graph topologies. The CEG literature, through the stratified CEG class, has demonstrated efficacy over BNs in modelling processes with contextual independence structures.

CEGs are also suited to modelling ‘asymmetric’ processes with event spaces that do not admit a product space structure. While such processes are common in many domains, they are not easily and effectively modelled by BNs and other graphical models with variable-based topologies. This thesis presents the first exposition of the theory and applications of the more general non-stratified CEG class that models asymmetric processes. We demonstrate, through modelling of an asymmetric public health intervention, that the CEG provides a superior representation than the BN in non-product space settings.

We then present a novel dynamic variant of CEGs called the continuous time dynamic CEG which has an approximate semi-Markov process representation. We show that this dynamic class generalises and vastly expands the existing subclass of extended dynamic CEGs, first studied in Barclay et al. (2015). We develop semantics unique to this class and propose a dynamic inference scheme for it together with a novel continuous time probability propagation algorithm. In doing this, we are able to utilise any observed information about the temporal evolution of the process to update our beliefs.

Finally, we demonstrate by modelling the evolution of criminal collaborations how the Bayesian paradigm allows us to combine a dynamic CEG model with other disparate models – after due consideration of the independencies between these models – where each model is a component describing a distinct aspect of a complex longitudinal process.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Bayesian statistical decision theory -- Graphic methods, Mathematical statistics -- Data processing, Multivariate analysis -- Graphic methods, Probabilities
Official Date:	May 2021
Dates:	Date Event May 2021 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Mathematics for Real-World Systems Centre for Doctoral Training
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Smith, Jim Q.
Sponsors:	University of Warwick. Chancellor's International Scholarship
Extent:	xiv, 213 leaves : illustrations, charts
Language:	eng

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