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arXiv · 2311.14122

Decompositions of the mean continuous ranked probability score

Sebastian Arnold·Eva-Maria Walz·Johanna Ziegel·Tilmann Gneiting
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Abstract

The continuous ranked probability score (crps) is the most commonly used scoring rule in the evaluation of probabilistic forecasts for real-valued outcomes. To assess and rank forecasting methods, researchers compute the mean crps over given sets of forecast situations, based on the respective predictive distributions and outcomes. We propose a new, isotonicity-based decomposition of the mean crps into interpretable components that quantify miscalibration (MSC), discrimination ability (DSC), and uncertainty (UNC), respectively. In a detailed theoretical analysis, we compare the new approach to empirical decompositions proposed earlier, generalize to population versions, analyse their properties and relationships, and relate to a hierarchy of notions of calibration. The isotonicity-based decomposition guarantees the nonnegativity of the components and quantifies calibration in a sense that is stronger than for other types of decompositions, subject to the nondegeneracy of empirical decompositions. We illustrate the usage of the isotonicity-based decomposition in case studies from weather prediction and machine learning.

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Sebastian Arnold, Eva-Maria Walz, Johanna Ziegel, Tilmann Gneiting. 2023-11-23. Decompositions of the mean continuous ranked probability score. https://arxiv.org/abs/2311.14122

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