Incorporating Model Uncertainty into Spatial Predictions

Abstract

We consider a modeling approach for spatially distributed data. We are concerned with aspects of statistical inference for Gaussian random fields when the ultimate objective is to predict the value of the random field at unobserved locations. However the exact statistical model is seldom known before hand and is usually estimated from the very same data relative to which the predictions are made. Our objective is to assess the effect of the fact that the model is estimated, rather than known, on the prediction and the associated prediction uncertainty. We describe a method for achieving this objective. We, in essence, consider the best linear unbiased prediction procedure based on the model within a Bayesian framework.

These ideas are implemented for the spring temperature over the region in the northern United States based on the stations in the United States historical climatological network reported in Karl, Williams, Quinlan & Boden (1990).

This paper has benefited greatly from the guidance and suggestions of Michael Stein.