A 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 characterize the distribution of a random vector by its marginal distributions and a dependence measure: either productmoment 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. Specifically, we estimate the key properties of dependent input models with real-world data and construct a joint distribution by using the flexible NORmal To Anything (NORTA) representation. Then, we employ the bootstrap to capture the estimation error of the joint distributions, 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.