Variable selection for spatial random field predictors under a Bayesian mixed hierarchical spatial model

A health outcome can be observed at a spatial location and we wish to relate this to a set of environmental measurements made on a sampling grid. The environmental measurements are covariates in the model but due to the interpolation associated with the grid there is an error inherent in the covariate value used at the outcome location. Since there may be multiple measurements made on different covariates there could be considerable uncertainty in the covariate values to be used. In this paper we examine a Bayesian approach to the interpolation problem and also a Bayesian solution to the variable selection issue. We present a series of simulations which outline the problem of recovering the true relationships, and also provide an empirical example.