Estimating reliability and resolution of probability forecasts through decomposition of the empirical score

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Verified Uncertainty Calibration (2019, methodology): “An alternative estimator introduced in the meteorological literature [18, 19] reduces the bias of the plugin estimator; we prove that it achieves sample complexity that scales with p B by leveraging error cancellations across bins.”
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.”
Calibration tests in multi-class classification: A unifying framework (2019, methodology): “Sample complexity bounds for a bias-reduced estimator of the ECE introduced in metereological literature (Bröcker, 2011; Ferro and Fricker, 2012) were derived in concurrent work (Kumar et al., 2019).”
A bias‐corrected decomposition of the Brier score (2012, methodology): “Bröcker (2011) showed that the three terms in the Brier score decomposition (1) are biased.”