Abstract
For modeling spatial processes, we propose a rich parametric class of stationary range anisotropic covariance structures that, when applied in R2, 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 Matérn 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.
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Ecker, M.D., Gelfand, A.E. Spatial modeling and prediction under stationary non-geometric range anisotropy. Environmental and Ecological Statistics 10, 165–178 (2003). https://doi.org/10.1023/A:1023600123559
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DOI: https://doi.org/10.1023/A:1023600123559