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Extensive scoring rules

机译：广泛的评分规则

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Scoring rules evaluate the performance of probabilistic forecasts. A scoring rule is said to be local if it assigns a score based on the observed outcome and on outcomes that are in some sense “close” to the observed outcome. All scoring rules can be derived from a concave entropy functional and the property of locality follows when the entropy is 1-homogeneous (up to an additive constant). Consequently, except for the log score, a local scoring rule has the remarkable property that it is 0-homogeneous; in other words, it assigns a score that is independent of the normalization of the quoted probability distribution. In many statistical applications, it is not plausible to treat observed outcomes as independent, e.g. time series data or multicomponent measurements. We show that local scoring rules can be easily extended to multidimensional outcome spaces. We also introduce the notion of an extensive scoring rule, i.e. a scoring rule that ensures the score of independent outcomes is a sum of independent scores. We construct local scoring rules that are extensive and show that a scoring rule is a extensive if and only if it is derived from an extensive entropy.
机译：计分规则评估概率预测的性能。如果评分规则根据观察到的结果以及在某种意义上与观察到的结果“接近”的结果分配分数，则称该评分规则是局部的。所有评分规则都可以从凹熵函数导出，并且当熵为1均匀（直到加法常数）时，局部性也随之变化。因此，除了对数分数外，局部计分规则具有显着的性质，即它是0均匀的。换句话说，它分配的分数与引用的概率分布的规范化无关。在许多统计应用中，将观察到的结果视为独立的结果是不合理的。时间序列数据或多分量测量。我们表明，本地评分规则可以轻松地扩展到多维结果空间。我们还介绍了广泛的评分规则的概念，即确保独立结果得分是独立得分之和的得分规则。我们构造了广泛的局部计分规则，并表明，当且仅当计分规则是从广泛的熵派生的，它才是广泛的。

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