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.

翻译：恰当评分规则近年来受到越来越多的关注，不仅作为概率预测的评估工具，也作为估计概率分布的方法。本文回顾了恰当评分规则的数学基础，包括一般特征化结果和重要的评分规则族。我们讨论了它们在统计学与机器学习中用于估计和预测评估的作用。此外，我们还评述了其在实际应用中值得关注的发展趋势。