Optimal network design for spatial prediction, covariance parameter estimation, and empirical prediction

Inferences for spatial data are affected substantially by the spatial configuration of the network of sites where measurements are taken. In this article, criteria for network design that emphasize the utility of the network for prediction (kriging) of unobserved responses assuming known spatial covariance parameters are contrasted with criteria that emphasize the estimation of the covariance parameters themselves. It is shown, via a series of related examples, that these two main design objectives are largely antithetical and thus lead to quite different "optimal" designs. Furthermore, a hybrid design criterion that accounts for the effect that the sampling variation of spatial covariance parameter estimates has on prediction is described and illustrated. Situations in which the hybrid optimal design resembles designs that are optimal with respect to each of the other two criteria are identified. An application to the optimal augmentation of an acid deposition monitoring network in the eastern US is presented.