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Customising structure of graphical models
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Wilkerson, Rachel Lynne (2020) Customising structure of graphical models. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3715190
Abstract
Graphical models have proven useful in a wide variety of applications. However, too often the structure of the graphical model is secondary consideration selected for convenience. This thesis makes the case that the chosen structure of the graphical model is fundamental to the resultant analysis. The motivation for this thesis stems from a desire to translate the dynamics described by domain experts into customised statistical models. In this thesis I propose a toolkit for systematically considering other model classes.
The domain of food insecurity motivates the development of models beyond the BN. The examples are illustrated with four graphical model classes: Bayesian Networks, Chain Event Graphs, Multi-regression Dynamic Models, and Flow Graphs. We argue that the problem dynamics should be considered before selecting the model class.
The tree-based Chain Event Graph class of models has proven to be particularly useful for applications in which experts describe a series of events. For this class of models, full checks on the structure are developed, both in the form of theoretical advances in a d-separation theorem and in technical model diagnostics. The full d-separation criteria can be used to verify that the conditional independence relationships implied by the graphs are consistent with the information expressed only through its topology and colouring. The theorem also confirms that using CEG d-separation, conditional independence relationships that cannot be represented by the Bayesian network are expressible in the CEG. The suite of diagnostic monitors check the accuracy of the forecasts that flow from the model. Examining increasingly fine elements of the CEG structure offers checks to see how well the model is consistent with observations.
Finally, we conclude by considering alternative graphical structures offers nuanced expressions of causation most suitable to certain statistical models. We examine again the four classes of models to illustrate how causal concepts like instrumental variables and intervention become richer in alternative classes of models.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Graph theory, Graphical modeling (Statistics), Bayesian statistical decision theory, Trees (Graph theory), Mathematical statistics -- Graphic methods, Food security -- Graphic methods | ||||
Official Date: | March 2020 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Statistics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Smith, J. Q., 1953- ; Uprichard, Emma | ||||
Sponsors: | Leverhulme Trust | ||||
Format of File: | |||||
Extent: | xv, 143 leaves : illustrations | ||||
Language: | eng |
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