Space filling and locally optimal designs for Gaussian Universal Kriging

Computer simulations are often used to replace physical experiments aimed at exploring the complex relationships between input and output variables. Undoubtedly, computer experiments have several advantages over real ones, however, when the response function is complex, simulation runs may be very expensive and/or time-consuming, and a possible solution consist of approximating the simulator by a suitable stochastic metamodel, simpler and much faster to run. Several metamodel techniques have been suggested in the literature and one of the most popular is the Kriging methodology. In this paper we study the optimal design problem for the Universal Kriging metamodel with respect to different approaches, related to prediction, information gain and estimation. Also we give further justifications and some criticism concerning the adoption of the space filling designs, based on theoretical results and numerical evidence as well.