Our paper Decomposing Probabilistic Scores: Reliability, Information Loss and Uncertainty, with Agathe Fernandes-Machado, is now available https://doi.org/10.48550/arXiv.2603.15232

Calibration is a conditional property that depends on the information retained by a predictor. We develop decomposition identities for arbitrary proper losses that make this dependence explicit. At any information level \mathcal{A}, the expected loss of an \mathcal{A}-measurable predictor splits into a proper-regret (reliability) term and a conditional entropy (residual uncertainty) term. For nested levels \mathcal{A}\subset\mathcal{B}, a chain decomposition quantifies the information gain from \mathcal{A} to \mathcal{B}. Applied to classification with features \boldsymbol{X} and score S=s(\boldsymbol{X}), this yields a three-term identity: miscalibration, a {\em grouping} term measuring information loss from \boldsymbol{X}  to {S}, and irreducible uncertainty at the feature level. We leverage the framework to analyze post-hoc recalibration, aggregation of calibrated models, and stagewise/boosting constructions, with explicit forms for Brier and log-loss.