Bayesian perspectives on statistical modelling

Polson, Nicholas G. (1988) Bayesian perspectives on statistical modelling. PhD thesis, University of Nottingham.

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Abstract

This thesis explores the representation of probability measures in a coherent Bayesian modelling framework, together with the ensuing characterisation properties of posterior functionals.

First, a decision theoretic approach is adopted to provide a unified modelling criterion applicable to assessing prior-likelihood combinations, design matrices, model dimensionality and choice of sample size. The utility structure and associated Bayes risk induces a distance measure, introducing concepts from differential geometry to aid in the interpretation of modelling characteristics.

Secondly, analytical and approximate computations for the implementation of the Bayesian paradigm, based on the properties of the class of transformation models, are discussed.

Finally, relationships between distance measures (in the form of either a derivative of a Bayes mapping or an induced distance) are explored, with particular reference to the construction of sensitivity measures.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Smith, A.F.M.
Keywords: Bayesian statistical decision theory, statistical modelling
Subjects: Q Science > QA Mathematics > QA276 Mathematical statistics
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 11292
Depositing User: EP, Services
Date Deposited: 21 May 2010 13:25
Last Modified: 15 Sep 2016 07:29
URI: http://eprints.nottingham.ac.uk/id/eprint/11292

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