Proper scoring rules are an essential tool to assess the predictive performance of probabilistic forecasts. However, propriety alone does not ensure an informative characterization of predictive performance and it is recommended to compare forecasts using multiple scoring rules. With that in mind, interpretable scoring rules providing complementary information are necessary. We formalize a framework based on aggregation and transformation to build interpretable multivariate proper scoring rules. Aggregation-and-transformation-based scoring rules are able to target specific features of the probabilistic forecasts; which improves the characterization of the predictive performance. This framework is illustrated through examples taken from the literature and studied using numerical experiments showcasing its benefits. In particular, it is shown that it can help bridge the gap between proper scoring rules and spatial verification tools.

翻译：严格评分规则是评估概率预测性能的重要工具。然而，仅具备严格性并不能确保对预测性能提供充分的表征，因此建议使用多种评分规则对预测进行比较。基于此，需要能够提供互补信息的可解释评分规则。我们形式化了一个基于聚合与变换的框架，用于构建可解释的多元严格评分规则。基于聚合与变换的评分规则能够针对概率预测的特定特征，从而改进对预测性能的表征。该框架通过文献中的实例加以说明，并利用数值实验研究展示了其优势。特别地，研究表明该框架有助于弥合严格评分规则与空间验证工具之间的差距。