Scoring rules serve to quantify predictive performance. A scoring rule is proper if truth telling is an optimal strategy in expectation. Subject to customary regularity conditions, every scoring rule can be made proper, by applying a special case of the Bayes act construction studied by Grünwald and Dawid (Ann Stat 32:1367–1433, 2004 ) and Dawid (Ann Inst Stat Math 59:77–93, 2007 ), to which we refer as properization. We discuss examples from the recent literature and apply the construction to create new types, and reinterpret existing forms, of proper scoring rules and consistent scoring functions. In an abstract setting, we formulate sufficient conditions under which Bayes acts exist and scoring rules can be made proper.

中文翻译：

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Properization：通过贝叶斯行为构建适当的评分规则

评分规则用于量化预测性能。如果说实话是预期的最佳策略，则评分规则是正确的。根据习惯规律性条件，通过应用 Grünwald 和 Dawid (Ann Stat 32:1367–1433, 2004 ) 和 Dawid (Ann Inst Stat Math 59:77) 研究的贝叶斯行为结构的特殊情况，可以使每个评分规则都合适–93, 2007 )，我们称之为适当化。我们讨论了最近文献中的例子，并应用该结构来创建新类型，并重新解释适当评分规则和一致评分函数的现有形式。在抽象的环境中，我们制定了贝叶斯行为存在的充分条件，并且可以制定适当的评分规则。