ABSTRACT
The Bayesian hierarchical modelling framework allows us to build a model for a complex spatial-temporal data structure in a modular fashion. Models can be created by using the models discussed up to this point – the spatial models of Chapters 7 and 8 – to describe the overall spatial pattern common to all time points and the temporal models of Chapter 12 to describe the overall temporal pattern common to all spatial units. A sensible starting point is to combine a spatial model with a temporal model and to build a model that belongs to the class of space-time separable models. This is the purpose of this chapter. The chapter considers two ways of combining a spatial model with a temporal model – additively or multiplicatively – and explains why combining the two models additively is, in most practical applications, more appropriate. To illustrate the modelling, we analyse the annual burglary count data observed at the small area level in Peterborough, England, over the period 2001 to 2008. The goal of the analysis is to estimate the annual small area burglary rates. A number of space-time separable models that are candidates for meeting the goal of the analysis are presented. We provide detail on how to fit one of the candidate models to the burglary data in WinBUGS. Through this application, we reveal the importance of a space-time separable model to the process of modelling spatial-temporal data.
