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The iterated auxiliary particle filter and applications to state space models and diffusion processes.
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Guarniero, Pieralberto (2017) The iterated auxiliary particle filter and applications to state space models and diffusion processes. PhD thesis, University of Warwick.
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WRAP_Theses_ Guarniero _2017.pdf - Submitted Version - Requires a PDF viewer. Download (4012Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3111801~S15
Abstract
The novel research work presented in this thesis consists of an offline, iterated particle filter to facilitate statistical inference in general state space hidden Markov models. Given a model and a sequence of observations, the associated marginal likelihood L is central to likelihood-based inference for unknown statistical parameters. We define a class of “twisted” models: each member is specified by a sequence of positive functions ψ and has an associated ψ - auxiliary particle filter that provides unbiased estimates of L. We identify a sequence ψ* that is optimal in the sense that the ψ* -auxiliary particle filter’s estimate of L has zero variance. In practical applications, ψ* is unknown so the ψ* - auxiliary particle filter cannot straightforwardly be implemented. We use an iterative scheme to approximate ψ*, and demonstrate empirically that the resulting iterated auxiliary particle filter significantly outperforms the most popular competitors in some challenging settings. Applications include parameter estimation using a particle Markov chain Monte Carlo algorithm. An adaptation of the iAPF for statistical inference in the context of diffusion processes along with a number of examples and applications in this setting is provided
| Item Type: | Thesis or Dissertation (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Diffusion processes, Markov processes | ||||
| Official Date: | August 2017 | ||||
| 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| Publication Status: | Unpublished | ||||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. | ||||
| Extent: | 141 leaves : charts. | ||||
| Language: | eng |
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