A Bayesian Nonparametric Framework for Uncertainty Quantification in Simulation.

When we use simulation to assess the performance of stochastic systems, the input models used to drive simulation experiments are often estimated from finite real-world data. There exist both input and simulation estimation uncertainty in the system performance estimates. Without strong prior information on the input models and the system mean response surface, in this paper, we propose a Bayesian nonparametric framework to quantify the impact from both sources of uncertainty. Specifically, nonparametric input models are introduced to faithfully capture the important features of the real-world data, such as heterogeneity, multi-modality and skewness. Bayesian posteriors of flexible input models characterize the input uncertainty, which automatically accounts for both model selection and parameter value uncertainty. Then, the input uncertainty is propagated to outputs by using direct simulation. Thus, under very general conditions, our framework delivers an empirical credible interval accounting for both input and simulation uncertainties. A variance decomposition is further developed to quantify the relative contributions from both sources of uncertainty. Our approach is supported by rigorous theoretical and empirical study.