Title: Proper scoring rules for estimation and forecast evaluation Show Chinese title

Title: 用于估计和预测评估的合理评分规则

Abstract: Proper scoring rules have been a subject of growing interest in recent years, not only as tools for evaluation of probabilistic forecasts but also as methods for estimating probability distributions. In this article, we review the mathematical foundations of proper scoring rules including general characterization results and important families of scoring rules. We discuss their role in statistics and machine learning for estimation and forecast evaluation. Furthermore, we comment on interesting developments of their usage in applications. Show Chinese abstract

Abstract: 适当评分规则近年来引起了越来越多的关注，不仅作为评估概率预测的工具，也作为估计概率分布的方法。 在本文中，我们回顾了适当评分规则的数学基础，包括一般的表征结果和重要的评分规则族。 我们讨论了它们在统计学和机器学习中用于估计和预测评估的作用。 此外，我们对它们在应用中的有趣发展进行了评论。