Bayesian Interpolation Schemes for Monitoring Systems

Environmental monitoring gives rise to several statistical problems of optimal design. We study the question of interpolation from a Bayesian point of view. Although the considered models are motivated by applications we focus on a theoretical concept rather than the presentation of case studies. We derive Bayesian estimates and risks for variables of interest in monitoring systems under conjugate priors for multivariate normal distributions. Numerical approaches such as MCMC algorithms are discussed in addition.