A Bayesian model for the unlabelled size-and-shape analysis
This thesis considers the development of efficient MCMC sampling methods for Bayesian models used for the pairwise alignment of two unlabelled configurations. We introduce ideas from differential geometry along with other recent developments in unlabelled shape analysis as a means of creating novel...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
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2018
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| Online Access: | https://eprints.nottingham.ac.uk/55511/ |
| _version_ | 1848799175622262784 |
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| author | Sajib, Anamul |
| author_facet | Sajib, Anamul |
| author_sort | Sajib, Anamul |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This thesis considers the development of efficient MCMC sampling methods for Bayesian models used for the pairwise alignment of two unlabelled configurations. We introduce ideas from differential geometry along with other recent developments in unlabelled shape analysis as a means of creating novel and more efficient MCMC sampling methods for such models. For example, we have improved the performance of the sampler for the model of Green and Mardia (2006) by sampling rotation, A ∈ SO(3), and matching matrix using geodesic Monte Carlo (MCMC defined on manifold) and Forbes and Lauritzen (2014) matching sampler, developed for finger print matching problem, respectively.
We also propose a new Bayesian model, together with implementation methods, motivated by the desire for further improvement. The model and its implementation methods proposed exploit the continuous nature of the parameter space of our Bayesian model and thus move around easily in this continuous space, providing highly efficient convergence and exploration of the target posterior distribution. The proposed Bayesian model and its implementation methods provide generalizations of the existing two models, Bayesian Hierarchical and regression models, introduced by Green and Mardia (2006) and Taylor, Mardia and Kent (2003) respectively, and resolve many shortcomings of existing implementation methods; slow convergence, traps in local mode and dependence on initial starting values when sampling from high dimensional and multi-modal posterior distributions. We illustrate our model and its implementation methods on the alignment of two proteins and two gels, and we find that the performance of proposed implementation methods under proposed model is better than current implementation techniques of existing models in both real and simulated data sets. |
| first_indexed | 2025-11-14T20:31:29Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-55511 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:31:29Z |
| publishDate | 2018 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-555112025-02-28T14:17:58Z https://eprints.nottingham.ac.uk/55511/ A Bayesian model for the unlabelled size-and-shape analysis Sajib, Anamul This thesis considers the development of efficient MCMC sampling methods for Bayesian models used for the pairwise alignment of two unlabelled configurations. We introduce ideas from differential geometry along with other recent developments in unlabelled shape analysis as a means of creating novel and more efficient MCMC sampling methods for such models. For example, we have improved the performance of the sampler for the model of Green and Mardia (2006) by sampling rotation, A ∈ SO(3), and matching matrix using geodesic Monte Carlo (MCMC defined on manifold) and Forbes and Lauritzen (2014) matching sampler, developed for finger print matching problem, respectively. We also propose a new Bayesian model, together with implementation methods, motivated by the desire for further improvement. The model and its implementation methods proposed exploit the continuous nature of the parameter space of our Bayesian model and thus move around easily in this continuous space, providing highly efficient convergence and exploration of the target posterior distribution. The proposed Bayesian model and its implementation methods provide generalizations of the existing two models, Bayesian Hierarchical and regression models, introduced by Green and Mardia (2006) and Taylor, Mardia and Kent (2003) respectively, and resolve many shortcomings of existing implementation methods; slow convergence, traps in local mode and dependence on initial starting values when sampling from high dimensional and multi-modal posterior distributions. We illustrate our model and its implementation methods on the alignment of two proteins and two gels, and we find that the performance of proposed implementation methods under proposed model is better than current implementation techniques of existing models in both real and simulated data sets. 2018-12-11 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/55511/1/Final_Corr_Thes.pdf Sajib, Anamul (2018) A Bayesian model for the unlabelled size-and-shape analysis. PhD thesis, University of Nottingham. Bayesian models; Differential geometry; Unlabelled shape analysis |
| spellingShingle | Bayesian models; Differential geometry; Unlabelled shape analysis Sajib, Anamul A Bayesian model for the unlabelled size-and-shape analysis |
| title | A Bayesian model for the unlabelled size-and-shape analysis |
| title_full | A Bayesian model for the unlabelled size-and-shape analysis |
| title_fullStr | A Bayesian model for the unlabelled size-and-shape analysis |
| title_full_unstemmed | A Bayesian model for the unlabelled size-and-shape analysis |
| title_short | A Bayesian model for the unlabelled size-and-shape analysis |
| title_sort | bayesian model for the unlabelled size-and-shape analysis |
| topic | Bayesian models; Differential geometry; Unlabelled shape analysis |
| url | https://eprints.nottingham.ac.uk/55511/ |