In stochastic simulation, input uncertainty refers to the propagation of the statistical noise in calibrating input models to impact output accuracy, in addition to the Monte Carlo simulation noise. The vast majority of the input uncertainty literature focuses on estimating target output quantities that are real-valued. However, outputs of simulation models are random and real-valued targets essentially serve only as summary statistics. To provide a more holistic assessment, we study the input uncertainty problem from a distributional view, namely we construct confidence bands for the entire output distribution function. Our approach utilizes a novel test statistic whose asymptotic consists of the supremum of the sum of a Brownian bridge and a suitable mean-zero Gaussian process, which generalizes the Kolmogorov-Smirnov statistic to account for input uncertainty. Regarding implementation, we also demonstrate how to use subsampling to efficiently estimate the covariance function of the Gaussian process, thereby leading to an implementable estimation of the quantile of the test statistic and a statistically valid confidence band. Numerical results demonstrate how our new confidence bands provide valid coverage for output distributions under input uncertainty that is not achievable by conventional approaches.

翻译：在随机仿真中，输入不确定性是指除蒙特卡洛仿真噪声外，输入模型标定过程中的统计噪声传播对输出精度的影响。绝大多数输入不确定性研究聚焦于估计取实数值的目标输出量，然而仿真模型的输出是随机的，实数值目标本质上仅作为汇总统计量。为提供更全面的评估，我们从分布视角研究输入不确定性，即为整个输出分布函数构建置信带。该方法采用一种新型检验统计量，其渐近形态由布朗桥与合适零均值高斯过程之和的上确界构成，将Kolmogorov-Smirnov统计量推广至可处理输入不确定性。在实现方面，我们进一步展示如何通过子抽样法高效估计高斯过程的协方差函数，从而实现对检验统计量分位数的可操作估计与统计有效的置信带。数值结果表明，新置信带能在输入不确定性下为输出分布提供传统方法无法实现的有效覆盖。