基于适当评分规则的信号噪声比泛化
A generalisation of the signal-to-noise ratio using proper scoring rules
AI总结：
本文基于适当评分规则泛化信号噪声比概念，通过数值实例展示其在集合预报和二元事件概率预报中的应用，揭示不同统计特性。
摘要：
本文提供了一种信号噪声比（或等价的可预测成分比，RPC）的泛化概念，基于适当评分规则。该定义是经典RPC的自然扩展，允许对任何可评分的预报类型定义和分析信号噪声特性，从而大大扩展了这些概念的应用范围。通过集合预报和二元事件概率预报的数值实例，使用连续排名概率分数（CRPS）和对数得分进行评分。数值示例使用了具有预设信号噪声比的合成数据以及北大西洋振荡（NAO）指数的季节性集合回顾预测。后者以前被解释为具有信号噪声“悖论”或异常信号噪声比，使用RPC统计量。对于合成数据，RPC统计量和基于评分规则的统计量在哪些数据集表现出异常信号噪声比上一致，但显示出不同的方差，表明不同的统计特性。对于NAO数据，不同统计量在信号噪声比是否异常上更为模棱两可。
英文摘要：
A generalised concept of the signal-to-noise ratio (or equivalently the ratio of predictable components, or RPC) is provided, based on proper scoring rules. This definition is the natural generalisation of the classical RPC, yet it allows one to define and analyse the signal-to-noise properties of any type of forecast that is amenable to scoring, thus drastically widening the applicability of these concepts. The methodology is illustrated through numerical examples of ensemble forecasts, scored using the continuous ranked probability score (CRPS), and of probability forecasts of a binary event, scored using the logarithmic score. Numerical examples are carried out using both synthetic data with prescribed signal-to-noise ratios as well as seasonal ensemble hindcasts of the North Atlantic Oscillation (NAO) index. The latter have previously been interpreted as having a signal-to-noise "paradox", or anomalous signal-to-noise ratio, using the RPC statistic. For the synthetic data, the RPC statistic as well as the scoring rule-based ones agree regarding which data sets exhibit anomalous signal-to-noise ratios, but exhibit different variance, indicating different statistical properties. For the NAO data, on the other hand, the different statistics are more equivocal on whether the signal-to-noise ratio is anomalous.
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