Investigation of Bayesian spatial models

The popularity of Bayesian disease mapping is increasing, as is the variety of available models. The most commonly used prior for enabling spatial correlation within a Bayesian model is the intrinsic conditional autoregressive (CAR) distribution. This approach allows for local smoothing of estimates over neighbouring areas, but it assumes a common variance for the smoothing term over the whole region. This is applicable if there is a smooth spatial trend over the region, which may not be valid for large, spatially heterogeneous areas. The aim of this report is to critically review alternative Bayesian models, especially those that enable local variation in the smoothing.