拆解贝叶斯评分，让预测优劣一目了然
An intuitive rearranging of the Yates covariance decomposition for probabilistic verification of forecasts with the Brier score
- 将贝叶斯评分分解为方差、相关性、均值三项非负分量
- 完美预测需同时匹配结果的方差、相关性和均值
- 适合评估概率预测模型的可解释性与改进方向
合理评分规则对评估概率预测至关重要。我们提出一种贝叶斯评分耶茨协方差分解的简单代数重排，将其分为三个独立非负项：方差不匹配项、相关性不足项和校准整体项。该重排使完美预测的最优条件清晰可见：最优预测必须同时匹配结果的方差、实现与结果的完全正相关，并匹配结果的均值。任何偏离这些条件都会导致贝叶斯评分的正向贡献。
原文摘要 · Abstract (English)
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.
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