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Keywords:

  • Conditional auto-regressive priors;
  • Disease mapping;
  • Integrated nested Laplace approximations;
  • Spatial correlation

Summary

Conditional auto-regressive models are commonly used to capture spatial cor relation in areal unit data, as part of a hierarchical Bayesian model. The spatial correlation structure that is induced by these models is determined by geographical adjacency, but this is too simplistic for some real data sets, which can visually exhibit subregions of strong correlation as well as locations at which the response exhibits a step change. An example of this, and the motivation for the paper, is the spatial pattern in respiratory disease risk in the 271 intermed iate geographies in the Greater Glasgow and Clyde Health Board in 2005. The methodology proposed is an extension to the class of conditional auto-regressive priors, which allow them to capture such localized spatial correlation and to identify step changes. The approach takes the form of an iterative algorithm, which sequentially updates the spatial correlation structure that is 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.