Locally adaptive spatial smoothing using conditional auto-regressive models

Conditional autoregressive (CAR) models are commonly used to capture spatial correlation in areal unit data, as part of a hierarchical Bayesian model. The spatial correlation structure induced by these models is determined by geographical adjacency, but this is too simplistic for some real datasets, which can visually exhibit sub-regions of strong correlation as well as locations at which the response exhibits a step-change. An example of this, and the motivation for this paper, is the spatial pattern in respiratory disease risk in the 271 Intermediate Geographies in the Greater Glasgow and Clyde Health board in 2005, which is displayed in Figure 2. The methodology proposed is an extension to the class of CAR priors, which allow them to capture such localised spatial correlation and identify step changes. The approach takes the form of an iterative algorithm, which sequentially updates the spatial correlation structure assumed by the model in addition to estimating the remaining parameters. The efficacy of the approach is assessed by simulation, before being applied to the motivating Greater Glasgow application