Finke, Axel (2015) On extended state-space constructions for monte carlo methods. PhD thesis, University of Warwick.

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Abstract

This thesis develops computationally efficient methodology in two areas. Firstly, we consider a particularly challenging class of discretely observed continuous-time point-process models. For these, we analyse and improve an existing filtering algorithm based on sequential Monte Carlo (smc) methods. To estimate the static parameters in such models, we devise novel particle Gibbs samplers. One of these exploits a sophisticated non-entred parametrisation whose benefits in a Markov chain Monte Carlo (mcmc) context have previously been limited by the lack of blockwise updates for the latent point process. We apply this algorithm to a Lévy-driven stochastic volatility model. Secondly, we devise novel Monte Carlo methods – based around pseudo-marginal and conditional smc approaches – for performing optimisation in latent-variable models and more generally. To ease the explanation of the wide range of techniques employed in this work, we describe a generic importance-sampling framework which admits virtually all Monte Carlo methods, including smc and mcmc methods, as special cases. Indeed, hierarchical combinations of different Monte Carlo schemes such as smc within mcmc or smc within smc can be justified as repeated applications of this framework.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	State-space methods, Monte Carlo method
Official Date:	July 2015
Dates:	Date Event July 2015 Submitted
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Johansen, Adam ; Spanò, Dario
Sponsors:	Engineering and Physical Sciences Research Council
Extent:	xxv, 216 leaves : charts
Language:	eng

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