Efficient model-fitting and model-comparison for high-dimensional Bayesian geostatistical models

Geostatistical models are appropriate for spatially distributed data measured at irregularly spaced locations. We propose an efficient Markov chain Monte Carlo (MCMC) algorithm for fitting Bayesian geostatistical models with substantial numbers of unknown parameters to sizable data sets. The algorithm facilitates use of MCMC sampler output for computing Bayes factors for model selection. In our illustrative analysis of an environmental data set, model selection is critical because the inference of primary interest changes depending on whether the model includes or ignores spatial correlation.