Empirical Bayes regionalization methods for spatial stochastic processes

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Abstract
Many geophysical properties can be described as spatial stochastic processes, including spatially correlated hydraulic conductivity fields. Use of regional data can potentially improve estimation of such processes. We consider the case in which observations at each of several sites are described by a general linear model, while the parameters of these models arise from a common regional distribution. Parametric empirical Bayes methods enable the determination of the parameters of the regional distribution via maximum likelihood. However, such methods have not been utilized for spatial stochastic processes. We develop the application of a simple iterative technique for maximum likelihood estimation of the regional parameters, and demonstrate its use with a common parameterization of the spatial covariance structure. Synthetic data tests show the potential for substantial reduction in estimation risk through use of such techniques.