Epidemic models and MCMC inference

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Abstract

Statistical inference and model choice for partially observed epidemics provide a variety of challenges both practical and theoretical. This thesis studies some related aspects of models for epidemics and their inference.

The use of the matrix exponential to facilitate exact calculations in the General Stochastic Epidemic (GSE) is demonstrated, most usefully in providing the exact marginal likelihood when infection times are unobserved.

The bipartite graph epidemic is defined and shown to be a flexible framework which encompasses many existing models. It also provides a way in which a deeper understanding of the relation between existing models could be obtained.

The Indian buffet epidemic is introduced as a non-parametric approach to modelling unknown heterogeneous contact structures in epidemics. Inference for the Indian buffet epidemic is a challenging problem, some progress has been made. However the algorithms which have been studied do not yet scale to the size of problem where significant differences from the GSE are apparent.

Evidence confirming and demonstrating the importance of understanding the tail behaviour of proposals in importance sampling is presented. The adverse impact of heavy tailed proposals on the Grouped Independence Metropolis-Hastings (GIMH) and Monte Carlo within Metropolis (MCWM) algorithms is demonstrated.

A new algorithm, the Kernel Metropolis Hastings (KMH), is proposed as an approximate algorithm for low dimensional marginal inference in situations where the GIMH algorithm fails because of sticking. The KMH is demonstrated on a challenging 2-d problem.

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