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Abstract:
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Computer experiments have become ubiquitous in science and engineering. For expensive or time-consuming stochastic simulations, stochastic kriging (Ankenman, et al. (2010)) is commonly used to generate predictions. Here, we decompose error in stochastic kriging predictions into nominal, numeric, parameter estimation and parameter estimation numeric components and provide means to control each in terms of properties of the underlying experimental design. The design properties implied for each source of error are weakly conflicting and several broad principles are proposed. In brief, the space-filling properties "small fill distance" and "large separation distance" should balance with replication at unique input configurations, with number of replications depending on the relative magnitudes of the stochastic and process variability, while non-stationarity implies more input density in more active regions and regression functions imply a push towards balancing with traditional design properties. This work can be applied to the deterministic case proposed in Haaland et al. (2014). A few examples are presented to illustrate the results.
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