  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 model and simulation estimation
uncertainties 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, since the real-world data often
represent the variability caused by various latent sources of uncertainty,
Dirichlet Processes Mixtures (DPM) based nonparametric input models are
introduced to model a mixture of heterogeneous distributions, which can
faithfully capture the important features of real-world data, such as
multi-modality and skewness. Bayesian posteriors of flexible input models
characterize the input model estimation uncertainty, which automatically
accounts for both model selection and parameter value uncertainty. Then, input
model estimation 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.
