Building Accurate Emulators for Stochastic Simulations via Quantile Kriging

Abstract

Computer simulation has increasingly become popular for analysis of systems that cannot be feasibly changed because of costs or scale. This work proposes a method to construct an emulator for stochastic simulations by performing a designed experiment on the simulator and developing an emulative distribution. Existing emulators have focused on estimation of the mean of the simulation output, but this work presents an emulator for the distribution of the output. This construction provides both an explicit distribution and a fast sampling scheme. Beyond the emulator description, this work demonstrates the emulator’s efficiency, that is, its convergence rate is the asymptotically optimal among all possible emulators using the same sample size (under certain conditions). An example of its practical use is demonstrated using a stochastic simulation of fracture mechanics. Supplementary materials for this article are available online.

KEY WORDS:

• Computer experiments
• Gaussian process
• Metric entropy
• Quantile regression
• Reproducing kernel Hilbert spaces
• Simulation experiments

Acknowledgments

Plumlee’s research is supported by the National Science Foundation grant CMMI-1030125. Tuo’s research is supported by NSF grants DMS-0705261 and 1007574, and National Natural Science Foundation of China 11271355. The authors also thank C.F. Jeff Wu, V. Roshan Joesph, three anonymous reviewers, and the AE for their helpful comments on this work.