We consider the estimation of small probabilities or other risk quantities associated with rare but catastrophic events. In the model-based literature, much of the focus has been devoted to efficient Monte Carlo computation or analytical approximation assuming the model is accurately specified. In this paper, we study a distinct direction on the propagation of model uncertainty and how it impacts the reliability of rare-event estimates. Specifically, we consider the basic setup of the exceedance of i.i.d. sum, and investigate how the lack of tail information of each input summand can affect the output probability. We argue that heavy-tailed problems are much more vulnerable to input uncertainty than light-tailed problems, reasoned through their large deviations behaviors and numerical evidence. We also investigate some approaches to quantify model errors in this problem using a combination of the bootstrap and extreme value theory, showing some positive outcomes but also uncovering some statistical challenges.

翻译：我们考虑与罕见但灾难性事件相关的小概率或其他风险量的估计问题。在基于模型的研究中，大量工作集中于假设模型准确指定下的高效蒙特卡洛计算或解析近似。本文研究了一个不同的方向——模型不确定性的传播及其对罕见事件估计可靠性的影响。具体而言，我们以独立同分布随机变量和的超越概率为基本框架，探究每个输入加数的尾部信息缺失如何影响输出概率。我们通过大偏差行为分析与数值实验证明：重尾问题对输入不确定性的敏感度远高于轻尾问题。此外，我们结合自助法与极值理论探讨了量化此类问题中模型误差的若干方法，不仅展示了部分积极成果，也揭示了若干统计挑战。