A Bayesian model for the unlabelled size-and-shape analysis

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Sajib, Anamul (2018) A Bayesian model for the unlabelled size-and-shape analysis. PhD thesis, University of Nottingham.

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Abstract

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.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Fallaize, Christopher
Brignell, Christopher J.
Keywords: Bayesian models; Differential geometry; Unlabelled shape analysis
Subjects: Q Science > QA Mathematics > QA276 Mathematical statistics
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 55511
Depositing User: Sajib, Anamul
Date Deposited: 06 Feb 2019 13:25
Last Modified: 07 Feb 2019 18:01
URI: https://eprints.nottingham.ac.uk/id/eprint/55511

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