概率预报性能的有效序贯推理
Valid sequential inference on probability forecast performance
摘要：
二元事件的概率预报在许多应用中起着核心作用。它们的质量通常通过适当的评分规则进行评估，该规则为预测分配数值分数，以便正确的预测达到最低预期分数。在本文中，我们构造了e值，用于检验序列设置中竞争预测的得分差异的统计显著性。E值已被提出作为假设检验的p值的替代，并且它们可以通过取乘法逆而容易地转换为保守的p值。本文中提出的e值在有限样本中有效，而无需对数据生成过程进行任何假设。它们还允许可选的停止，因此预测用户可以在任何时候考虑可用数据决定中断评估，并且仍然可以得出统计上有效的推断，这对于基于经典p值的测试通常是不正确的。在降水预报后处理的案例研究中，最先进的预报优势检验和e值得出了相同的结论。
英文摘要：
Probability forecasts for binary events play a central role in many applications. Their quality is commonly assessed with proper scoring rules, which assign forecasts a numerical score such that a correct forecast achieves a minimal expected score. In this paper, we construct e-values for testing the statistical significance of score differences of competing forecasts in sequential settings. E-values have been proposed as an alternative to p-values for hypothesis testing, and they can easily be transformed into conservative p-values by taking the multiplicative inverse. The e-values proposed in this article are valid in finite samples without any assumptions on the data generating processes. They also allow optional stopping, so a forecast user may decide to interrupt evaluation taking into account the available data at any time and still draw statistically valid inference, which is generally not true for classical p-value based tests. In a case study on postprocessing of precipitation forecasts, state-of-the-art forecasts dominance tests and e-values lead to the same conclusions.
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