This thesis has two related aims: establishing tractable conditions for posterior consistency of statistical inference from non-IID data with an intractable likelihood, and developing Monte Carlo methodology for conducting such inference. Two prominent classes of models, jump diffusions and generalised coalescent processes, are considered throughout. Both are motivated by population genetics applications. Posterior consistency of nonparametric inference is established for joint inference of drift and compound Poisson jump components of unit volatility jump diffusions in arbitrary dimension under an identifiability assumption. This assumption is straightforward to verify in the diffusion case, but difficult to check in general for jump diffusions. A similar consistency result is established under somewhat weaker conditions for Λ-coalescent processes whenever time series data is available. I also show that Λ-coalescent inference cannot be consistent if observations are contemporaneous, in stark contrast to the more classical case of the Kingman coalescent. I also introduce the notion of reverse time sequential Monte Carlo (SMC), which has previously been applied to Kingman and Λ-coalescents. Here, reverse time SMC is presented as a generic algorithm, and general conditions under which it is effective are developed. In brief, it is well suited to integration over paths which begin at a mode of the target distribution, and terminate in the tails. These innovations are used to design new SMC algorithms for generalised coalescent processes, as well as non-coalescent examples including evaluating a containment probability of the hyperbolic diffusion, an overflow probability in a queueing model and finding an initial infection in an epidemic network model.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:714888 |
| Date | January 2016 |
| Creators | Koskela, Jere |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/88065/ |
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