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Title: Some new results in sequential Monte Carlo
Author: Martin, James Stewart
ISNI:       0000 0004 2741 6444
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2012
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Sequential Monte Carlo (SMC) methods have been well studied within the context of performing inference with respect to partially observed Markov processes, and their use in this context relies upon the ability to evaluate or estimate the likelihood of a set of observed data, given the state of the latent process. In many real-world applications such as the study of population genetics and econometrics, however, this likelihood can neither be analytically evaluated nor replaced by an unbiased estimator, and so the application of exact SMC methods to these problems may be infeasible, or even impossible. The models in many of these applications are complex, yet realistic, and so development of techniques that can deal with problems of likelihood intractability can help us to perform inference for many important yet otherwise inaccessible problems; this motivates the research presented within this thesis. The main focus of this work is the application of approximate Bayesian computation (ABC) methodology to state-space models (SSMs) and the development of SMC methods in the context of these ABC SSMs for filtering and smoothing of the latent process. The introduction of ABC here avoids the need to evaluate the likelihood, at the cost of introducing a bias into the resulting filtering and smoothing estimators; this bias is explored theoretically and through simulation studies. An alternative SMC procedure, incorporating an additional rejection step, is also considered and the novel application of this rejection-based SMC procedure to the ABC approximation of the SSM is considered. This thesis will also consider the application of MCMC and SMC methods to a class of partially observed point process (PP) models. We investigate the problem of performing sequential inference for these models and note that current methods often fail. We present a new approach to smoothing in this context, using SMC samplers (Del Moral et al., 2006). This approach is illustrated, with some theoretical discussion, on a doubly stochastic PP applied in the context of finance.
Supervisor: McCoy, Emma Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral