Some advances in Bayesian spatial prediction and sampling design

The goal of the present paper is to report on some recent advances, which we have made over the last five years, in spatial interpolation and sampling design in case of uncertainty about the parameters of common geostatistical models and non-Gaussianity of observations. In particular, we consider copula-based approaches to spatial interpolation when the observations are distinctly non-Gaussian and then report on criteria and methods for choosing default priors for Bayesian spatial interpolation and for choosing optimal designs based on (transformed) Gaussian kriging. For most of the interpolation and design methods presented in this paper we provide free source code in MATLAB/Octave language.