A bias‐corrected decomposition of the Brier score

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Verified Uncertainty Calibration (2019, background): “Alternatively, [18, 19] propose to subtract an approximation of the bias from the estimate: Definition 5.”
The Matthews Correlation Coefficient (MCC) is More Informative Than Cohen’s Kappa and Brier Score in Binary Classification Assessment (2021, methodology): “The theme of the Brier score decomposition was treated again in the correspondence article of Young [91], in an correspondence article by Ferro and Fricker [92], in a letter by Siegert [93], and in a study by Merkle and Hartman [94].”
Mitigating bias in calibration error estimation (2020, methodology): “We consider two estimators previously proposed in the literature: the debiased estimator (Brocker, 2012; Ferro and Fricker, 2012), which we refer to as ECEdebias, and the smoothed kernel density estimator of Zhang et al.”
Probabilistic quantitative precipitation forecasting using Ensemble Model Output Statistics (2013, methodology): “We add this information to our diagrams, using a slightly different decomposition proposed by Ferro and Fricker (2012), which is less biased in finite samples and therefore provides a more accurate measure of performance.”
Calibration tests in multi-class classification: A unifying framework (2019, methodology): “As Gretton et al. (2012), we make use of symmetrization ideas (van der Vaart and Wellner, 1996, p.”