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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:682855 |
| Date | January 2015 |
| Creators | Finke, Axel |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/77119/ |
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