Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.665424
Title: Exploring complex loss functions for point estimation
Author: Chaisee, Kuntalee
ISNI:       0000 0004 5349 055X
Awarding Body: University of Bath
Current Institution: University of Bath
Date of Award: 2015
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Abstract:
This thesis presents several aspects of simulation-based point estimation in the context of Bayesian decision theory. The first part of the thesis (Chapters 4 - 5) concerns the estimation-then-minimisation (ETM) method as an efficient computational approach to compute simulation-based Bayes estimates. We are interested in applying the ETM method to compute Bayes estimates under some non-standard loss functions. However, for some loss functions, the ETM method cannot be implemented straightforwardly. We examine the ETM method via Taylor approximations and cubic spline interpolations for Bayes estimates in one dimension. In two dimensions, we implement the ETM method via bicubic interpolation. The second part of the thesis (Chapter 6) concentrates on the analysis of a mixture posterior distribution with a known number of components using the Markov chain Monte Carlo (MCMC) output. We aim for Bayesian point estimation related to a label invariant loss function which allows us to estimate the parameters in the mixture posterior distribution without dealing with label switching. We also investigate uncertainty of the point estimates which is presented by the uncertainty bound and the crude uncertainty bound of the expected loss evaluated at the point estimates based on MCMC samples. The crude uncertainty bound is relatively cheap, but it seems to be unreliable. On the other hand, the uncertainty bound which is approximated a 95% confidence interval seems to be reliable, but are very computationally expensive. The third part of the thesis (Chapter 7), we propose a possible alternative way to present the uncertainty for Bayesian point estimates. We adopt the idea of leaving out observations from the jackknife method to compute jackknife-Bayes estimates. We then use the jackknife-Bayes estimates to visualise the uncertainty of Bayes estimates. Further investigation is required to improve the method and some suggestions are made to maximise the efficiency of this approach.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.665424  DOI: Not available
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