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This paper presents a robust version of the stratified sampling method whenmultiple uncertain input models are considered for stochastic simulation.Various variance reduction techniques have demonstrated their superiorperformance in accelerating simulation processes. Nevertheless, they often usea single input model and further assume that the input model is exactly knownand fixed. We consider more general cases in which it is necessary to assess asimulation's response to a variety of input models, such as when evaluating thereliability of wind turbines under nonstationary wind conditions or theoperation of a service system when the distribution of customer inter-arrivaltime is heterogeneous at different times. Moreover, the estimation variance maybe considerably impacted by uncertainty in input models. To address suchnonstationary and uncertain input models, we offer a distributionally robust(DR) stratified sampling approach with the goal of minimizing the maximum ofworst-case estimator variances among plausible but uncertain input models.Specifically, we devise a bi-level optimization framework for formulating DRstochastic problems with different ambiguity set designs, based on the$L_2$-norm, 1-Wasserstein distance, parametric family of distributions, anddistribution moments. In order to cope with the non-convexity of objectivefunction, we present a solution approach that uses Bayesian optimization.Numerical experiments and the wind turbine case study demonstrate therobustness of the proposed approach.

Distributionally Robust Stratified Sampling for Stochastic Simulations with Multiple Uncertain Input Models