Bayesian Network Designs for Fields with Unknown Variance Function

We consider the problem of designing a network of sampling locations in a spatial domain that will be used to interpolate a spatial field. We focus on the random field model in which variance is given by an unknown step function of the locations. We express this uncertainty through an appropriate class of prior distributions and introduce a Bayesian sequential sampling algorithm. At each step, posterior parameter values are updated through realizations from previously selected locations. We examine the convergence of parameter estimates. We discuss the improvement of the Bayesian method over conventional sampling techniques for different prior distributions and cardinalities of the design network.