Measuring the Uncertainty in Kriging

Abstract

Spatial phenomena is commonly modelled as a realization from a stochastic process. Even when the reality is unique such models can usefully represent the uncertainty the modeler has about the phenomena. This paper is concerned with predicting for Gaussian random fields in a way that appropriately deals with uncertainty in the covariance function. To this end, we analyze the best linear unbiased prediction procedure (kriging) within a Bayesian framework. Particular attention is paid to the treatment of parameters in the covariance structure and their effect on the quality, both real and perceived, of the prediction. We show how this model can be improved by accounting for the uncertainty in the model parameters.