Quantifying statistical uncertainty for dependent input models with factor structure

Abstract

Simulation used for the performance assessment of stochastic systems is usually driven by input models estimated from real-world data, which introduces both input and simulation uncertainty to the performance estimates. For many complex systems, because the components of input models are mutually dependent, an efficient estimation of dependence could improve the system performance assessment. Since the dependence could be caused by underlying common factors, we explore Gaussian copula factor models to characterize input models with dependence. We propose a Bayesian framework to quantify both input and simulation uncertainty. The input uncertainty is quantified by the posterior of input models and then propagated to output means by direct simulation, with the simulation estimation error characterized by the posterior distributions of system mean responses. This Bayesian framework delivers credible intervals that quantify the overall uncertainty of system performance estimates. Our approach is supported by both asymptotic theory and empirical study.