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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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
1988
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| Online Access: | https://eprints.nottingham.ac.uk/11292/ |
| _version_ | 1848791240767700992 |
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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. |
| first_indexed | 2025-11-14T18:25:22Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-11292 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:25:22Z |
| publishDate | 1988 |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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/ |