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Scoring rules like the Brier Score (Mean Squared Error, Quadratic Score) and Log Loss (Cross-Entropy, Negative Log-Likelihood, Logarithmic Score) can favor incorrect predictions. To address this limitation, the Probabilistic Brier Score (PBS) and Probabilistic Logarithmic Loss (PLL) have been introduced for probabilistic classifiers.
Do published probabilistic forecasts hold up when you score them? Pre-registered verification of NWS precipitation, AirNow air quality, and CAISO day-ahead power prices — one scoring toolkit, three domains.