Controlling Sources of Inaccuracy in Stochastic Kriging

ABSTRACT

Scientists and engineers commonly use simulation models to study real systems for which actual experimentation is costly, difficult, or impossible. Many simulations are stochastic in the sense that repeated runs with the same input configuration will result in different outputs. For expensive or time-consuming simulations, stochastic kriging is commonly used to generate predictions for simulation model outputs subject to uncertainty due to both function approximation and stochastic variation. Here, we develop and justify a few guidelines for experimental design, which ensure accuracy of stochastic kriging emulators. 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 broad principles are proposed. In brief, space-filling properties, “small fill distance” and “large separation distance,” should be balanced with replication at distinct input configurations, with number of replications depending on the relative magnitudes of stochastic and process variability. Nonstationarity implies higher input density in more active regions, while regression functions imply a balance with traditional design properties. A few examples are presented to illustrate the results. Supplementary materials providing proofs of the theoretical results and code for comparisons are available online.

KEYWORDS:

• Computer experiment
• Emulation
• Experimental design
• Gaussian process
• Stochastic kriging

Supplementary Materials

• Supplementary Materials: (pdf) Proofs of the theoretical results; (zip) R code for comparisons.

Acknowledgments

The authors thank the editor, associate editor, and two anonymous referees for their insightful comments and suggestions that have greatly improved this manuscript. The authors gratefully acknowledge funding from NSF DMS-1621722 and DMS-1739097.