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An intuitive rearranging of the Yates covariance decompos...
[Submitted on 4 Mar 2026 (v1), last revised 22 Jun 2026 (this ve · 2026-06-23 · via stat updates on arXiv.org

Authors:Bruno Hebling Vieira (Methods of Plasticity Research, Department of Psychology, University of Zurich, Zurich, Switzerland)

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Abstract:Proper scoring rules are essential for evaluating probabilistic forecasts. We propose a simple algebraic rearrangement of the Yates covariance decomposition of the Brier score into three independently non-negative terms: a variance mismatch term, a correlation deficit term, and a calibration-in-the-large term. This rearrangement makes the optimality conditions for perfect forecasting transparent: the optimal forecast must simultaneously match the variance of outcomes, achieve perfect positive correlation with outcomes, and match the mean of outcomes. Any deviation from these conditions results in a positive contribution to the Brier score.

Submission history

From: Bruno Hebling Vieira [view email]
[v1] Wed, 4 Mar 2026 15:37:00 UTC (6 KB)
[v2] Mon, 22 Jun 2026 07:36:56 UTC (6 KB)