Building Accurate Emulators for Stochastic Simulations via Quantile Kriging

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.