Multivariate Input Uncertainty in Output Analysis for Stochastic Simulation

When we use simulations to estimate the performance of stochastic systems, the simulation is often driven by input models estimated from finite real-world data. A complete statistical characterization of system performance estimates requires quantifying both input model and simulation estimation errors. The components of input models in many complex systems could be dependent. In this paper, we represent the distribution of a random vector by its marginal distributions and a dependence measure: either product-moment or Spearman rank correlations. To quantify the impact from dependent input model and simulation estimation errors on system performance estimates, we propose a metamodel-assisted bootstrap framework that is applicable to cases when the parametric family of multivariate input distributions is known or unknown. In either case, we first characterize the input models by their moments that are estimated using real-world data. Then, we employ the bootstrap to quantify the input estimation error, and an equation-based stochastic kriging metamodel to propagate the input uncertainty to the output mean, which can also reduce the influence of simulation estimation error due to output variability. Asymptotic analysis provides theoretical support for our approach, while an empirical study demonstrates that it has good finite-sample performance.