Predicting the Output From a Stochastic Computer Model When a Deterministic Approximation is Available

Abstract

Statistically modeling the output of a stochastic computer model can be difficult to do accurately without a large simulation budget. We alleviate this problem by exploiting readily available deterministic approximations to efficiently learn about the respective stochastic computer models. This is done via the summation of two Gaussian processes; one responsible for modeling the deterministic approximation, the other responsible for using such approximation to better statistically model the stochastic computer model. The developed method provides high predictive performance and increased confidence that complicated features of a stochastic computer model are captured, even when the simulation budget is small. Several synthetic computer models are used to outline the capabilities of this method, and two real-world examples are used to display its practical utility. Supplementary materials for this article are available online.