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Title: Some novel Monte Carlo algorithms for challenging inference problems
Author: Marshall, Tristan Roy Gray
ISNI:       0000 0004 2724 9236
Awarding Body: Lancaster University
Current Institution: Lancaster University
Date of Award: 2009
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This work consists of two separate parts. In the first part we extend the work on exact simulation of diffusions introduced in [9]. The authors in that paper introduced a methodology for simulating a diffusion process and for performing parametric inference for a partially observed diffusion. In particular they demonstrated how to perform Bayesian inference for a parameter θ of such a diffusion; it is possible to implement a Gibbs Sampler that alternately imputes the paths between observed points conditionally on θ, and updating for θ conditionally on the imputed paths. , This algorithm simulates values (θn)n≥l whose distribution converges to the true posterior in the n→t ∞ limit; we extend their algorithm to simulate exact samples from the posterior within a finite time - so-called perfect simulation. In the second part we consider a class of adaptive MCMC algorithms using a Langevin-type proposal density. We state and prove regularity conditions for the convergence of these algorithms. In addition to these theoretical results we introduce a number of methodological innovations that can be applied much more generally. We assess the performance of these algorithms with simulation studies, including an example of the statistical analysis of a point process driven by a latent log-Gaussian Cox process.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available