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Monte Carlo methods based on novel classes of regeneration-enriched Markov processes
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McKimm, Hector (2022) Monte Carlo methods based on novel classes of regeneration-enriched Markov processes. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3921792~S15
Abstract
Enriching some underlying continuous-time Markov process with regenerations from a fixed regeneration distribution µ at a particular regeneration rate Ƙ results in a Markov process that has a target distribution π as its invariant distribution. Firstly, we introduce a method for adapting the regeneration distribution, which allows a significantly smaller regeneration rate to be used, which makes simulation feasible for a wider range of target distributions. The regeneration distribution is adapted on-the-fly, by adding point masses to it. Secondly, we show that a class of non- π -invariant jump processes, which are defined on an augmented statespace and have a jump chain transition kernel corresponding to a deterministic, invertible mapping, may be enriched with regenerations so that the resulting process is π -invariant. Since the underlying jump process does not need to be π invariant, its dynamics may be chosen to use gradient information to guide the process to areas of high probability mass, which makes the sampler a promising algorithm for multi-modal target distributions.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Monte Carlo method, Markov processes, Jump processes | ||||
Official Date: | September 2022 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Statistics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Roberts, Gareth O. ; Pollock, Murray | ||||
Sponsors: | Engineering and Physical Sciences Research Council | ||||
Extent: | xii, 158 pages : illustrations, charts | ||||
Language: | eng |
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