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Resampling and genealogies in sequential Monte Carlo algorithms
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Brown, Susanna Elizabeth (2021) Resampling and genealogies in sequential Monte Carlo algorithms. PhD thesis, University of Warwick.
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WRAP_Theses_Brown_S_2021.pdf - Submitted Version - Requires a PDF viewer. Download (1044Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3765741~S15
Abstract
This thesis attempts to quantify the problem of ancestral degeneracy of sequential Monte Carlo samples, which is known to have a critical effect on the performance of the resulting estimators. To facilitate comparisons between different algorithms, the induced genealogical processes are analysed under an asymptotic regime in which the number of particles tends to infinity. Simple conditions are derived under which these genealogical processes converge weakly to Kingman's well-studied n-coalescent, with a certain time change. These sufficient conditions are verified for many of the most popular sequential Monte Carlo algorithms, giving a novel insight into the large-sample behaviour of the associated estimators. The asymptotic regime serves to unify these different algorithms
in one framework, the genealogical differences between the algorithms then being fully captured by the respective time-change functions. The results also have implications in theoretical population genetics, where the processes studied may be seen as population models involving selection. Our main theorem then comprises a novel weak convergence result for genealogies arising from non-neutral populations.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Monte Carlo method, Algorithms, Sequences (Mathematics) | ||||
Official Date: | August 2021 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Statistics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Jenkins, Paul ; Koskela, Jere ; Johansen, Adam M. | ||||
Sponsors: | Engineering and Physical Sciences Research Council | ||||
Extent: | xviii, 121 leaves : charts | ||||
Language: | eng |
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