Spatial modeling and prediction under stationary non-geometric range anisotropy

For modeling spatial processes, we propose a rich parametric class of stationary range anisotropic covariance structures that, when applied in R-2, greatly increases the scope of variogram contors. Geometric anisotropy, which provides the most common generalization of isotropy within stationarity, is a special case. Our class is built from monotonic isotropic correlation functions and special cases include the Matern and the general exponential functions. As a result, our range anisotropic correlation specification can be attached to a second order stationary spatial process model, unlike ad hoc approaches to range anisotropy in the literature. We adopt a Bayesian perspective to obtain full inference and demonstrate how to fit the resulting model using sampling-based methods. In the presence of measurement error/microscale effect, we can obtain both the usual predictive as well as the noiseless predictive distribution. We analyze a data set of scallop catches under the general exponential range anisotropic model, withholding ten sites to compare the accuracy and precision of the standard and noiseless predictive distributions.