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When we use simulation to assess the performance of stochastic systems, theinput models used to drive simulation experiments are often estimated fromfinite real-world data. There exist both input model and simulation estimationuncertainties in the system performance estimates. Without strong priorinformation on the input models and the system mean response surface, in thispaper, we propose a Bayesian nonparametric framework to quantify the impactfrom both sources of uncertainty. Specifically, since the real-world data oftenrepresent the variability caused by various latent sources of uncertainty,Dirichlet Processes Mixtures (DPM) based nonparametric input models areintroduced to model a mixture of heterogeneous distributions, which canfaithfully capture the important features of real-world data, such asmulti-modality and skewness. Bayesian posteriors of flexible input modelscharacterize the input model estimation uncertainty, which automaticallyaccounts for both model selection and parameter value uncertainty. Then, inputmodel estimation uncertainty is propagated to outputs by using directsimulation. Thus, under very general conditions, our framework delivers anempirical credible interval accounting for both input and simulationuncertainties. A variance decomposition is further developed to quantify therelative contributions from both sources of uncertainty. Our approach issupported by rigorous theoretical and empirical study.

A Nonparametric Bayesian Framework for Uncertainty Quantification in Stochastic Simulation