Some New Results in Sequential Monte Carlo
Author(s)
Martin, James Stewart
Type
Thesis
Abstract
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.
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.
Date Issued
2012-07
Date Awarded
2012-09
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
McCoy, Emma
Sponsor
Engineering and Physical Sciences Research Council
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)