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Sequential Monte Carlo variance estimators and global consensus
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Rendell, Lewis James (2020) Sequential Monte Carlo variance estimators and global consensus. PhD thesis, University of Warwick.
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WRAP_Theses_Rendell_2020.pdf - Submitted Version - Requires a PDF viewer. Download (2353Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3684525
Abstract
This thesis makes contributions in two main areas relating to sequential Monte Carlo (SMC) samplers, a class of sequential simulation algorithms used to approximate sequences of probability distributions defined on a common space. Firstly, we consider settings in which one has a single distribution of interest, from which obtaining samples using simple Markov chain Monte Carlo techniques may not be straightforward. We consider the problem of tuning an SMC sampler in this context, selecting an appropriate sequence of distributions to ensure efficient exploration of the space and to control the variance of the resulting estimators. We formalise this as a minimisation problem relating to an asymptotic variance, deriving expressions for a number of relevant quantities and solving this problem for some simple models. We also investigate procedures for selecting such a sequence in practice, utilising recently-proposed methods for cheaply estimating the variances of SMC-based estimators. Secondly, we consider the problem of approximating Bayesian posterior distributions, when these depend on large data sets distributed across multiple computers. Inspired by global variable consensus optimisation, we introduce a novel framework for simulation in distributed settings, proposing a Markov chain Monte Carlo algorithm on an extended state space. Based on the construction of an instrumental hierarchical model, a tuning parameter controls the fidelity to the original model. We also propose the use of these Markov kernels within an SMC sampler. We propose a method for using SMC variance estimators within a bias correction procedure, and propose a stopping rule for the SMC sampler, allowing the automatic selection of the tuning parameter. In contrast to similar distributed Monte Carlo algorithms, this approach requires few distributional assumptions. The performance of the algorithms is illustrated with a number of simulated examples.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Monte Carlo method, Sequences (Mathematics), Distribution (Probability theory), Algorithms, Markov processes | ||||
Official Date: | June 2020 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Statistics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Johansen, Adam M. ; Lee, Anthony W. L. | ||||
Sponsors: | Engineering and Physical Sciences Research Council | ||||
Format of File: | |||||
Extent: | xv, 198 leaves : illustrations | ||||
Language: | eng |
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