A practical problem in spatial statistics is that of constructing optimal sampling designs for spatial interpolation purposes. A wide range of methods used for constructing such designs are based on variogram-models fitting. Within this framework, we consider criteria that emphasize the use of coupled Gaussian processes for the spatial interpolation of a random field. Attention is largely focused on intrinsic processes which appear to be useful both for environmental monitoring and functional data analysis. The potential applications of these processes in sampling design will be shown through an extensive simulation study.

Keywords: Optimal sampling design, Gaussian processes, Increment processes, Derivative processes