Bayesian Variogram Modeling for an Isotropic Spatial Process

The variogram is a basic tool in geostatistics. In the case of an assumed isotropic process, it is used to compare variability of the difference between pairs of observations as a function of their distance. Customary approaches to variogram modeling create an empirical variogram and then fit a valid parametric or nonparametric variogram model to it. Here we adopt a Bayesian approach to variogram modeling. In particular, we seek to analyze a recent data set of scallop catches. We have the results of the analysis of an earlier data set from the region to supply useful prior information. In addition, the Bayesian approach enables inference about any aspect of spatial dependence of interest rather than merely providing a fitted variogram. We utilize discrete mixtures of Bessel functions which allow a rich and flexible class of variogram models. To differentiate between models, we introduce a utility based model choice criterion that encourages parsimony. We conclude with a fully Bayesian ..