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We derive intrinsic Kriging, using Matherons intrinsic random functions which eliminate the trend in classic Kriging. We formulate this intrinsic Kriging as a metamodel in deterministic and random simulation models. For random simulation we derive an experimental design that also specifies the number of replications that varies with the input combinations. We compare intrinsic Kriging and classic Kriging in several numerical experiments with deterministic and random simulations. These experiments suggest that intrinsic Kriging gives more accurate metamodel, in most experiments.

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Kriging (or a Gaussian process) provides metamodels for deterministic and random simulation models. Actually, there are several types of Kriging; the classic type is the 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 weakens the Kriging metamodel.We therefore consider the so-called intrinsic Kriging (IK), which originated in geostatistics, and derive IK types for deterministic simulations and random simulations, respectively. 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 IK and classic Kriging, we use several numerical experiments with deterministic simulations and random simulations, respectively. These experiments show that IK gives better metamodels, in most experiments.

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