Optimal Network Designs for Spatial Prediction

A practical problem in spatial statistics is that of constructing spatial sampling designs for environmental monitoring networks. Among the several purposes for which a monitoring network may be designed for, there is that of interpolation. In this paper, a criterion for spatial designs that emphasize the utility of the network for spatial interpolation of a random field X is discussed. Within the Spatial Simulated Annealing (SSA), a stochastic algorithm devised for designing optimal sampling schemes, an R2 measure criterion is discussed as fitness function. Two different spatial interpolators, namely Kriging and Gaussian Markov Random Fields (GMRFs), are also considered and their potential applications in sampling designs discussed.