  We study an optimization-based approach to construct statistically accurate
confidence intervals for simulation performance measures under nonparametric
input uncertainty. This approach computes confidence bounds from simulation
runs driven by probability weights defined on the data, which are obtained from
solving optimization problems under suitably posited averaged divergence
constraints. We illustrate how this approach offers benefits in computational
efficiency and finite-sample performance compared to the bootstrap and the
delta method. While resembling robust optimization, we explain the procedural
design and develop tight statistical guarantees of this approach via a
generalization of the empirical likelihood method.
