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arXiv · 1102.5031

Local proper scoring rules of order two

Werner Ehm·Tilmann Gneiting
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Abstract

Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if it encourages truthful reporting. It is local of order $k$ if the score depends on the predictive density only through its value and the values of its derivatives of order up to $k$ at the realizing event. Complementing fundamental recent work by Parry, Dawid and Lauritzen, we characterize the local proper scoring rules of order 2 relative to a broad class of Lebesgue densities on the real line, using a different approach. In a data example, we use local and nonlocal proper scoring rules to assess statistically postprocessed ensemble weather forecasts.

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Werner Ehm, Tilmann Gneiting. 2011-02-24. Local proper scoring rules of order two. https://doi.org/10.1214/12-aos973

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