Interpolation with uncertain spatial covariances: A Bayesian alternative to Kriging

In this paper a Bayesian alternative to Kriging is developed. The latter is an important tool in geostatistics. But aspects of environmetrics make it less suitable as a tool for interpolating spatial random fields which are observed successively over time. The theory presented here permits temporal (and spatial) modeling to be done in a convenient and flexible way. At the same time model misspecifications, if any, can be corrected by additional data if and when it becomes available, and past data may be used in a systematic way to fit model parameters. Finally, uncertainty about model parameters is represented in the (posterior) distributions, so unrealistically small credible regions for the interpolants are avoided. The theory is based on the multivariate normal and related distributions, but because of the hierarchical prior models adopted, the results would seem somewhat robust with respect to the choice of these distributions and associated hyperparameters.