Statistical Methods for Complex Population Dynamics

Abstract

In recent years, the development of simulation-based, often approximate, statistical methods has been prompted by the challenges posed by complex models used in fields such ecology, epidemiology and system biology. A common issue with such models is that the likelihood function, so central to both Bayesian and classical approaches to statistical inference, is often unavailable or intractable. While intractable models could be dealt with using other methodologies, in this work we focus mainly on Synthetic Likelihood (SL). This is a simulation-based method based on summary statistics, rather than on the full data, and it is closely related to Approximate Bayesian Computation (ABC) methods.

The purpose of this thesis is twofold. First, we compare SL, ABC and other, less approximate, methods in the context of highly non-linear ecological and epidemiological models. We do this using a wide range of models, with both simulated and real data. The second part of the thesis is dedicated to improving SL. In particular, we address the computational cost of SL by proposing an efficient Maximum Synthetic Likelihood (MSL) algorithm, which exploits the Gaussian assumption used by SL. Finally, we relax this distributional assumption by proposing an original density estimator which, while being more flexible than a Gaussian estimator, scales well with the number of statistics used by SL.

Date of Award	31 Mar 2016
Original language	English
Awarding Institution	University of Bath
Sponsors	Engineering and Physical Sciences Research Council
Supervisor	Simon Wood (Supervisor)