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arXiv · 2509.03309

A Measure of Predictive Sharpness for Probabilistic Models

Pekka Syrjänen
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Abstract

We introduce a sharpness measure for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is constructed based on a rank-based concentration principle that tracks upward transfers of probability mass along the rearranged profile of the predictive distribution. For finite outcome spaces, this yields a normalized sharpness measure with transparent mass--length representation and equivalent formulations as a Gini-type coefficient on the probability vector and a scaled 1-Wasserstein distance from the uniform distribution in rearranged space. We extend the functional to continuous and multidimensional domains and establish normalization, symmetry, continuity, and monotonicity properties. We investigate the relationship between the measure and uncertainty and dispersion measures, and illustrate its diagnostic applications using real and simulated data.

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BibTeXRIS

Pekka Syrjänen. 2026-09-11. A Measure of Predictive Sharpness for Probabilistic Models. https://arxiv.org/abs/2509.03309

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