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

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.

若缺乏充足的仿真预算，精准对随机计算机模型（stochastic computer model）的输出开展统计建模往往颇具挑战。针对这一难题，我们通过利用现成可用的确定性近似（deterministic approximation），高效地对目标随机计算机模型展开研究。该方法通过构建两个高斯过程（Gaussian processes）的叠加模型实现：其中一个高斯过程用于对确定性近似项进行建模，另一个则借助该近似项，实现对随机计算机模型更精准的统计建模。所提出的方法不仅具备优异的预测性能，还能提升对随机计算机模型复杂特征被准确捕捉的置信度，即便在仿真预算有限的场景下亦是如此。我们采用多个合成计算机模型验证该方法的性能边界，并通过两个实际案例展示其实际应用价值。本文的补充材料可在线获取。