Bayesian perspectives on statistical modelling

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 assessin...

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Main Author: Polson, Nicholas G.
Format: Thesis (University of Nottingham only)
Language:English
Published: 1988
Subjects:
Online Access:https://eprints.nottingham.ac.uk/11292/
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author Polson, Nicholas G.
author_facet Polson, Nicholas G.
author_sort Polson, Nicholas G.
building Nottingham Research Data Repository
collection Online Access
description 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.
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format Thesis (University of Nottingham only)
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institution University of Nottingham Malaysia Campus
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language English
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publishDate 1988
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spelling nottingham-112922025-02-28T11:12:31Z https://eprints.nottingham.ac.uk/11292/ Bayesian perspectives on statistical modelling Polson, Nicholas G. 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. 1988 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/11292/1/384291.pdf Polson, Nicholas G. (1988) Bayesian perspectives on statistical modelling. PhD thesis, University of Nottingham. Bayesian statistical decision theory statistical modelling
spellingShingle Bayesian statistical decision theory
statistical modelling
Polson, Nicholas G.
Bayesian perspectives on statistical modelling
title Bayesian perspectives on statistical modelling
title_full Bayesian perspectives on statistical modelling
title_fullStr Bayesian perspectives on statistical modelling
title_full_unstemmed Bayesian perspectives on statistical modelling
title_short Bayesian perspectives on statistical modelling
title_sort bayesian perspectives on statistical modelling
topic Bayesian statistical decision theory
statistical modelling
url https://eprints.nottingham.ac.uk/11292/