Bayesian Approaches to Issues Arising in Spatial Modelling
Student: Earl Duncan
When: Friday, 7th April 2017 3:00 PM-4:00 PM
Where: GP-Z Block, Level 2, Room 207
- D/Prof Kerrie Mengersen (Principal)
- Dr Nicole White
- D/Prof Kerrie Mengersen (Chair)
- Dr Nicole White
- Prof Tony Pettit
- A/Prof Wenbiao Hu
This thesis aims to address several issues arising in the context of spatial modelling. Special focus is given to the analysis of spatio-temporal data in the context of mammography screening rates. To analyse this data, two sophisticated Bayesian hierarchical models are developed to answer specific research questions relating to the aberrant nature of temporal trends. In particular, the models are used to identify areas with associated temporal trends which may be considered aberrant, and highlight the spatial patterns of these areas. Understanding these patterns is an important initial step in identifying the reasons for service under-utilisation and aiding decision markers in the management and improvement of these services.
Two concepts which are fundamental to the methodology considered in the analysis of the mammography screening data are mixture models and spatial smoothing. Despite the vast literature on both concepts, there remain several important questions and opportunities for improving the methods. Mixture models allow for a more flexible model specification by describing the likelihood as a mixture of component densities. However, in the context of Bayesian estimation, the posterior distribution can become invariant to the permutations of the labels, which makes statistical inference difficult. The extent of label switching as an inferential problem and efficient, accurate solutions to this problem are just two examples of the research questions addressed by this thesis. On the concept of spatial smoothing, this thesis highlights the positive effect that spatial smoothing has on model fit and predictive ability, even when spatial autocorrelation of the observed data is not particularly strong. Various definitions of the smoothing weights are reviewed, and new alternatives are proposed, including the notion of covariate-based weights.