Cheap Bootstrap for Input Uncertainty Quantification

When a simulation model contains input distributions that need to be calibrated from external data, proper simulation output analysis needs to account for not only the noises from the Monte Carlo sample generation, but also the statistical noises from these input data. The latter issue is known commonly as the input uncertainty in the literature. An array of methods have been proposed to address input uncertainty, but one recurrent challenge faced by many of these methods is the demanding simulation load. In this paper, we present a method, based on a sort of modified bootstrap, to handle input uncertainty with multiplicatively less computation than these existing methods. In particular, this “cheap” bootstrap is able to construct confidence intervals that account for both input data and Monte Carlo noise efficiently by substantially reducing the number of outer samples in a nested procedure.