Scalable Bayesian inference for stochastic epidemic processes

The research reported in this thesis is motivated by the goal of using mathematical models to better understand the within-herd disease dynamics of Bovine tuberculosis (BTB) in UK cattle. This led to the development of new Bayesian methods and tools, including an open-source software package for Bayesian data analysis. In particular, those applicable to Discrete-state-space Partially Observed Markov Processes (DPOMP models). These were applied to the problem of model and parameter inference for a sample of individual herds selected from UK BTB surveillance records. Those findings led to the alternative models and methods utilised in the penultimate chapter, where we present a large scale, system-of-herds model and report novel parameter estimates for BTB. The latter include those that relate to disease detection; regional background risk; and farmer behaviour (specifically, the trading of live cattle). The work goes beyond previous, similar published research in three ways: it incorporates individual herd records, not just aggregated data; it includes formal methods of model assessment; that work is (partially) extended to systems comprising up to thousands of herds.