Efficient Input Uncertainty Quantification Via Green Simulation Using Sample Path Likelihood Ratios

Bootstrapping is a popular tool for quantifying input uncertainty, inflated uncertainty in the simulation output caused by finite-sample estimation error in the input models. Typical bootstrap-based procedures have a nested simulation structure that requires B × R simulation runs: the outer loop bootstraps B input distributions, each of which requires R inner simulation runs. In this article, we present a measure-theoretic framework for constructing a sample path likelihood ratio and propose an efficient input uncertainty quantification procedure using two green simulation estimators. The proposed procedures reuse the same R inner simulation outputs in all outer loops by reweighting them using appropriately defined likelihood ratios. Both procedures produce asymptotically valid confidence intervals for the expected simulation output under the true input distribution. Our numerical results show that the proposed procedures have efficiency gains compared to other popular bootstrap-based alternatives.