Random Perturbation and Bagging to Quantify Input Uncertainty

Henry Lam, Huajie Qian

Abstract: We consider the problem of estimating the output variance in simulation analysis that is contributed from the statistical errors in fitting the input models, the latter often known as the input uncertainty. This variance contribution can be written in terms of the sensitivity estimate of the output and the variance of the input distributions or parameters, via the delta method. We study the direct use of this representation in obtaining efficient estimators for the input-contributed variance, by using finite-difference and random perturbation to approximate the gradient, focusing especially in the nonparametric case. In particular, we analyze a particular type of random perturbation motivated from resampling that connects to an infinitesimal jackknife estimator used in bagging. We illustrate the optimal simulation allocation and the simulation effort complexity of this scheme, and show some supporting numerical results.