Abstract
For some years Markov chain Monte Carlo (MCMC) has been regarded as a central tool in computational statistics. Its principle shortcoming is that it requires evaluation of a likelihood term, which is commonly infeasible in practice for reasons of intractability or high dimensionality. Recent work on the so-called pseudo-marginal method [1, 2] has largely overcome this difficulty in settings where a positive, unbiased estimate of the likelihood is available. For state space models such an estimate is routinely calculated using sequential Monte Carlo methods. In combination the approach is termed particle Markov chain Monte Carlo (PMCMC).This thesis is principally concerned with developing a PMCMC method suitable for the sequentially Markov coalescent (SMC) [3,4],a model in population genetics for the ancestry of a set of sequences taken from a population. It is shown that the SMC can be recast as a piecewise deterministic Markov process and a novel particle filter is proposed for the case of two and three individuals. In particular the case of three individuals introduces a number of challenges that require bespoke solutions. These particle filter methods are then used in the context of a PMCMC algorithm to infer parameters of the biological model. Finally, backwards sampling is implemented in a non-trivial setting, and subsequently linked to very recent work [5] on pseudo-marginal algorithms that can scale well with the dimension of the problem, compared to traditional approaches.
| Date of Award | 6 Dec 2019 |
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| Original language | English |
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| Supervisor | Christophe Andrieu (Supervisor) & Mark A Beaumont (Supervisor) |