Verifying probabilistic forecasts for extreme events is a highly active research area because popular media and public opinions are naturally focused on extreme events, and biased conclusions are readily made. In this context, classical verification methods tailored for extreme events, such as thresholded and weighted scoring rules, have undesirable properties that cannot be mitigated, and the well-known continuous ranked probability score (CRPS) is no exception. In this paper, we define a formal framework for assessing the behavior of forecast evaluation procedures with respect to extreme events, which we use to demonstrate that assessment based on the expectation of a proper score is not suitable for extremes. Alternatively, we propose studying the properties of the CRPS as a random variable by using extreme value theory to address extreme event verification. An index is introduced to compare calibrated forecasts, which summarizes the ability of probabilistic forecasts for predicting extremes. The strengths and limitations of this method are discussed using both theoretical arguments and simulations.

翻译：验证极端事件的概率预报是一个高度活跃的研究领域，因为主流媒体和公众舆论自然关注极端事件，且容易得出有偏见的结论。在此背景下，针对极端事件设计的经典验证方法（如阈值化和加权评分规则）存在无法缓解的不良特性，而广为人知的连续排名概率得分（CRPS）也不例外。本文定义了一个评估预报验证程序在极端事件中表现的正式框架，用以证明基于适当评分期望的评估方法不适用于极端事件。作为替代方案，我们提出利用极值理论研究CRPS作为随机变量的性质，以解决极端事件验证问题。引入一个指标来比较经过校准的预报，该指标总结了概率预报预测极端事件的能力。通过理论论证与模拟研究，探讨了该方法的优势与局限性。