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 dataset of scallop catches. We have the results of the analysis of an earlier dataset 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 that 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 analysis of the scallop data.

Key Words
Bessel functions; Correlation functions; Importance sampling; Mixtures; Model determination; Stationary process

Mark D. Ecker is Assistant Professor, Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614-0506. Alan E. Gelfand is Professor, Department of Statistics, University of Connecticut, Storrs, CT 06269-3120.