Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts, existing evaluation techniques are ill-suited to the evaluation of tail properties of such forecasts. However, these tail properties are often of particular interest to forecast users due to the severe impacts caused by extreme outcomes. In this work, we introduce a general notion of tail calibration for probabilistic forecasts, which allows forecasters to assess the reliability of their predictions for extreme outcomes. We study the relationships between tail calibration and standard notions of forecast calibration, and discuss connections to peaks-over-threshold models in extreme value theory. Diagnostic tools are introduced and applied in a case study on European precipitation forecasts

翻译：概率预测全面描述了未知未来结果的不确定性，使其成为决策制定和风险管理的关键工具。尽管已有多种方法被提出用于评估概率预测，但现有的评估技术并不适用于评估此类预测的尾部特性。然而，由于极端结果可能造成的严重影响，这些尾部特性通常受到预测用户的特别关注。在本研究中，我们引入了概率预测尾部校准的一般概念，使预测者能够评估其对极端结果预测的可靠性。我们研究了尾部校准与标准预测校准概念之间的关系，并讨论了其与极值理论中峰值超阈值模型的联系。诊断工具被引入，并在欧洲降水预测的案例研究中得到应用。