Thwaites, Peter (2008) Chain event graphs : theory and application. PhD thesis, University of Warwick.

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Abstract

This thesis is concerned with the Graphical model known as the Chain Event Graph (CEG) [1][60][61], and develops the theory that appears in the currently published papers on this work. Results derived are analogous to those produced for Bayesian Networks (BNs), and I show that for asymmetric problems the CEG is generally superior to the BN both as a representation of the problem and as an analytical tool. The CEG is designed to embody the conditional independence structure of problems whose state spaces are asymmetric and do not admit a natural Product Space structure. In this they differ from BNs and other structures with variable-based topologies. Chapter 1 details researchers' attempts to adapt BNs to model such problems, and outlines the advantages CEGs have over these adaptations. Chapter 2 describes the construction of CEGs. In chapter 3I create a semantic structure for the reading of CEGs, and derive results expressible in the form of context-specific conditional independence statements, that allow us to delve much more deeply into the independence structure of a problem than we can do with BNs. In chapter 4I develop algorithms for the updating of a CEG following observation of an event, analogous to the Local Message Passing algorithms used with BNs. These are more efficient than the BN-based algorithms when used with asymmetric problems. Chapter 5 develops the theory of Causal manipulation of CEGs, and introduces the singular manipulation, a class of interventions containing the set of interventions possible with BNs. I produce Back Door and Front Door Theorems analogous to those of Pearl [42], but more flexible as they allow asymmetric manipulations of asymmetric problems. The ideas and results of chapters 2 to 5 are summarised in chapter 6.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Graphical modeling (Statistics)
Date:	April 2008
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Smith, J. Q., 1953-
Extent:	x, 197 leaves
Language:	eng
URI:	http://wrap.warwick.ac.uk/id/eprint/49194

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