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Monte Carlo methods for combining sample approximations of distributions
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Chan, Ryan Sze-Yin (2022) Monte Carlo methods for combining sample approximations of distributions. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3941627
Abstract
Combining several (sample approximations of) distributions, which we term sub-posteriors, into a single distribution proportional to their product, is a common challenge in statistics and data science. For instance, this can occur in distributed `big data' problems, tempering problems, or when working under multi-party privacy constraints. Many existing approaches resort to approximating the individual sub-posteriors for practical necessity, then finding either an analytical approximation or sample approximation of the resulting (product-pooled) posterior. The quality of the posterior approximation for these approaches is poor when the sub-posteriors fall out-with a narrow range of distributional form, such as being approximately Gaussian. Recently, a Fusion approach has been proposed which finds a direct and exact Monte Carlo approximation of the posterior (as opposed to the sub-posteriors), circumventing the drawbacks of approximate approaches. Unfortunately, existing Fusion approaches have a number of computational limitations, particularly when unifying a large number of sub-posteriors or when the sub-posteriors exhibit large correlation. In this thesis, we generalise the theory underpinning existing Fusion approaches, and embed the resulting methodology within a recursive divide-and-conquer sequential Monte Carlo paradigm. This ultimately leads to a competitive Fusion approach, which is appreciably more robust and scalable in a variety of practical settings.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Distribution (Probability theory), Monte Carlo method, Approximation theory, Statistical matching | ||||
Official Date: | October 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Publication Status: | Unpublished | ||||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: | Alan Turing Institute | ||||
Format of File: | |||||
Extent: | xiii, 201 pages : illustrations | ||||
Language: | eng |
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