Topics in statistics of spatial-temporal disease modelling

Abstract

This thesis is concerned with providing further statistical development in the area of space-time modelling with particular application to disease data. We briefly consider the non-Bayesian approaches of empirical mode decomposition and generalised linear modelling for analysing space-time data, but our main focus is on the increasingly popular Bayesian hierarchical approach and topics surrounding that. We begin by introducing the hierarchical Poisson regression model of Mugglin et al. [36] and a data set provided by NHS Direct which will be used to illustrate our results through-out the remainder of the thesis. We provide details of how a Bayesian analysis can be performed using Markov chain Monte Carlo (MCMC) via the software LinBUGS then go on to consider two particular issues associated with such analyses. Firstly, a problem with the efficiency of MCMC for the Poisson regression model is likely to be due to the presence of non-standard conditional distributions. We develop and test the 'improved auxiliary mixture sampling' method which introduces auxiliary variables to the conditional distribution in such a way that it becomes multivariate Normal and an efficient block Gibbs sampling scheme can be used to simulate from it. Secondly, since MCMC allows modelling of such complexity, inputs such as priors can only be elicited in a casual way thereby increasing the need to check how sensitive our output is to changes to the prior. We therefore develop and test the 'marginal sensitivity' method which, using only one MCMC output sample, quantifies how sensitive the marginal posterior distributions are to changes to prior parameters