Input Uncertainty Quantification Via Simulation Bootstrapping

Input uncertainty, which refers to the output variability arising from statistical noise in specifying the input models, has been intensively studied recently. Ignoring input uncertainty often leads to poor estimates of system performance. In the non-parametric setting, input uncertainty is commonly estimated via bootstrap, but the performance by traditional bootstrap resampling is compromised when input uncertainty is also associated with simulation uncertainty. Nested simulation is studied to improve the performance by taking variance estimation into account, but suffers from a substantial burden on required simulation effort. To tackle the above problems, this paper introduces a non-nested method to build asymptotically valid confidence intervals for input uncertainty quantification. The convergence properties are studied, which establish statistical guarantees for the proposed estimators related to real-data size and bootstrap budget. An easy-implemented algorithm is also provided. Numerical examples show that the estimated confidence intervals perform satisfactorily under given confidence levels.