Stochastic Intrinsic Kriging for Simulation Metamodelling

Kriging provides metamodels for deterministic and random simulation models. Actually, there are several types of Kriging; the classic type is so-called universal Kriging, which includes ordinary Kriging. These classic types require estimation of the trend in the input-output data of the underlying simulation model; this estimation deteriorates the Kriging metamodel. We therefore consider so-called intrinsic Kriging originating in geostatistics, and derive intrinsic Kriging for deterministic and random simulations. Moreover, for random simulations we derive experimental designs that specify the number of replications that varies with the input combination of the simulation model. To compare the performance
of intrinsic Kriging and classic Kriging, we use several numerical experiments with deterministic simulations and random simulations. These experiments show that intrinsic Kriging gives better metamodels, in most experiments.