Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.759673
Title: Adapting the Gibbs sampler
Author: Chimisov, Cyril
ISNI:       0000 0004 7431 7027
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2018
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Abstract:
In the present thesis, we close a methodological gap of optimising the basic Markov Chain Monte Carlo algorithms. Similarly to the straightforward and computationally efficient optimisation criteria for the Metropolis algorithm acceptance rate (and, equivalently, proposal scale), we develop criteria for optimising the selection probabilities of the Random Scan Gibbs Sampler. We develop a general purpose Adaptive Random Scan Gibbs Sampler, that adapts the selection probabilities, gradually, as further information is accrued by the sampler. We argue that Adaptive Random Scan Gibbs Samplers can be routinely implemented and substantial computational gains will be observed across many typical Gibbs sampling problems. Additionally, motivated to develop theory to analyse convergence properties of the Adaptive Gibbs Sampler, we introduce a class of Adapted Increasingly Rarely Markov Chain Monte Carlo (AirMCMC) algorithms, where the underlying Markov kernel is allowed to be changed based on the whole available chain output, but only at specific time points separated by an increasing number of iterations. The main motivation is the ease of analysis of such algorithms. Under regularity assumptions, we prove the Mean Square Error convergence, Weak and Strong Laws of Large Numbers, and the Central Limit Theorem and discuss how our approach extends the existing results. We argue that many of the known Adaptive MCMC algorithms may be transformed into the corresponding Air versions and provide an empirical evidence that performance of the Air version remains virtually the same.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council ; University of Warwick
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.759673  DOI: Not available
Keywords: QA Mathematics
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