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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2509.03309 |
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| _version_ | 1866915910009225216 |
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| author | Syrjänen, Pekka |
| author_facet | Syrjänen, Pekka |
| contents | We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived 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 bounded continuous and multidimensional domains for predictive distributions with finite first moment, and establish normalization, symmetry, continuity, and monotonicity properties. The diagnostic application of the measure is illustrated with real and simulated data, and a relationship to the multivariate energy score is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03309 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Measure of Predictive Sharpness for Probabilistic Models Syrjänen, Pekka Methodology We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived 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 bounded continuous and multidimensional domains for predictive distributions with finite first moment, and establish normalization, symmetry, continuity, and monotonicity properties. The diagnostic application of the measure is illustrated with real and simulated data, and a relationship to the multivariate energy score is discussed. |
| title | A Measure of Predictive Sharpness for Probabilistic Models |
| topic | Methodology |
| url | https://arxiv.org/abs/2509.03309 |