On the optimal designs for prediction of Ornstein-Uhlenbeck sheets

Computer simulations are often used to replace physical experiments to explore the complex relationships between input and output variables. We study the optimal design problem for prediction of a stationary Ornstein–Uhlenbeck sheet on a monotonic set with respect to integrated mean square prediction error and entropy criterion. We show that there is a substantial difference between the shapes of optimal designs for Ornstein–Uhlenbeck processes and sheets. In particular, we show that optimal prediction based on integrated mean square prediction error not necessary leads to space-filling designs.