ABSTRACT
This chapter considers spatial prediction, i.e., the prediction of the response variable at some, perhaps all, of the locations where it was not observed, which is also known as kriging. Classical theory and methodology of best linear unbiased prediction under a general linear model is reviewed and then specialized to spatial linear models with constant mean (ordinary kriging) or nonconstant mean (universal kriging). Other prediction-related topics considered include noiseless prediction, change-of-support prediction problems, the effects of covariance parameters on kriging, kriging versus inverse-distance weighting, the screening effect and negative kriging weights, and various practical issues. Then, cross-validation, which utilizes predictions based on fitted models to select among competing models, and conditional simulation, which uses a fitted model to repeatedly simulate complete spatial surfaces, are described. Finally, the methods are illustrated using three of the four data sets introduced in Chapter 1.
