Stochastic Kriging for Inadequate Simulation Models
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Stochastic kriging is a popular metamodeling technique for representing the unknown response surface of a simulation model. However, the simulation model may be inadequate in the sense that there may be a non-negligible discrepancy between it and the real system of interest. Failing to account for the model discrepancy may conceivably result in erroneous prediction of the real system's performance and mislead the decision-making process. Assuming the availability of physical observations of the real system, we propose a metamodel that extends stochastic kriging to incorporate the model discrepancy. The proposed metamodel utilizes both the simulation outputs and the real data to characterize the model discrepancy and can provably enhance the prediction of the real system's performance. We derive general results for experiment design and analysis, and demonstrate the advantage of the proposed metamodel relative to competing methods. Finally, we study the effect of Common Random Numbers (CRN). It is well known that the use of CRN is generally detrimental to the prediction accuracy of stochastic kriging. By contrast, we show that the effect of CRN in the new context is substantially more complex. The use of CRN can be either detrimental or beneficial depending on the interplay between the magnitude of the observation errors and other parameters involved.
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