Chain event graphs : theory and application
Thwaites, Peter (2008) Chain event graphs : theory and application. PhD thesis, University of Warwick.
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This thesis is concerned with the Graphical model known as the Chain Event Graph (CEG)
, 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 , 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)|
|Official Date:||April 2008|
|Institution:||University of Warwick|
|Theses Department:||Department of Statistics|
|Supervisor(s)/Advisor:||Smith, J. Q., 1953-|
|Extent:||x, 197 leaves|
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