Accounting for the uncertainty in the local mean in spatial prediction by Bayesian Maximum Entropy

Bayesian Maximum Entropy (BME) has been successfully used in geostatistics to calculate predictions of spatial variables given some general knowledge base and sets of hard (precise) and soft (imprecise) data. This general knowledge base commonly consists of the means at each of the locations considered in the analysis, and the covariances between these locations. When the means are not known, the standard practice is to estimate them from the data; this is done by either generalized least squares or maximum likelihood. The BME prediction then treats these estimates as the general knowledge means, and ignores their uncertainty. In this paper we develop a prediction that is based on the BME method that can be used when the general knowledge consists of the covariance model only. This prediction incorporates the uncertainty in the estimated local mean. We show that in some special cases our prediction is equal to results from classical geostatistics. We investigate the differences between our approach and the standard approach for predicting in this common practical situation.