论文标题
随机模拟的统计不确定性分析
Statistical Uncertainty Analysis for Stochastic Simulation
论文作者
论文摘要
当我们使用仿真来评估随机系统的性能时，模拟通常包含根据现实世界数据估算的输入分布。因此，性能估算中既存在模拟和输入不确定性。忽略任一个不确定性来源都低估了总体统计误差。通过其他计算（例如，更多复制）可以降低仿真不确定性。在可行的情况下，可以通过收集更多实际数据来减少输入不确定性。本文提出了一种量化整体统计不确定性的方法，当模拟由独立参数输入分布驱动时；具体而言，我们通过使用元模型辅助的引导方法来产生一个置信区间，该置信区间可以解释模拟和输入不确定性。输入不确定性是通过自举测量的，基于方程式的随机kriging metamodel传播了输入均值的输入不确定性，并且使用元模型的属性得出了模拟和元模型不确定性。提出了差异分解，以估计输入对总体不确定性的相对贡献；该信息表明，仅通过其他模拟，是否可以大大降低总体不确定性。渐近分析为我们的方法提供了理论支持，而一项经验研究表明，它具有良好的有限样本性能。
When we use simulation to evaluate the performance of a stochastic system, the simulation often contains input distributions estimated from real-world data; therefore, there is both simulation and input uncertainty in the performance estimates. Ignoring either source of uncertainty underestimates the overall statistical error. Simulation uncertainty can be reduced by additional computation (e.g., more replications). Input uncertainty can be reduced by collecting more real-world data, when feasible. This paper proposes an approach to quantify overall statistical uncertainty when the simulation is driven by independent parametric input distributions; specifically, we produce a confidence interval that accounts for both simulation and input uncertainty by using a metamodel-assisted bootstrapping approach. The input uncertainty is measured via bootstrapping, an equation-based stochastic kriging metamodel propagates the input uncertainty to the output mean, and both simulation and metamodel uncertainty are derived using properties of the metamodel. A variance decomposition is proposed to estimate the relative contribution of input to overall uncertainty; this information indicates whether the overall uncertainty can be significantly reduced through additional simulation alone. Asymptotic analysis provides theoretical support for our approach, while an empirical study demonstrates that it has good finite-sample performance.
