AI 中文总结
本研究提出了一种任意时间有效方法，用于证明预先指定的预测修正比未修正的源预测分布更优，该方法基于条件e过程，经实验验证可支持修正的有效性但无法唯一识别偏移机制。
AI 中文摘要
预测修正是对现有预测分布的预先指定修改，旨在反映给定输入下未来结果的预期变化，例如由仪器重新校准、检测漂移或已知干预措施引发。我们研究如何积累任意时间有效证据，以证明此类修正比未修正的源预测分布能更好地预测传入的目标结果。固定非负倾斜将源预测转换为修正预测，修正后与源的预测似然比是一个条件e值，其运行乘积构成e过程。该过程在可选停止和任意输入序列（包括自适应选择的序列）下保持有效，而其对数等于修正的累积预测对数得分优势。条件漂移分解描述了任意目标预测分布下的证据增长，依赖修正的半空间确定了 misspecified 目标分布，对于这些分布，相同的错误确认边界仍然成立。当预测似然比严格为正时，其倒数产生任意时间有效反驳边界，而超量恒等式解释了为何实现的零交叉概率可能低于名义水平。标签偏移、条件均值与方差、子组特定及指数族修正作为特例出现。预先指定的混合方法可容纳修正的不确定性，可预测倾斜允许自适应投注，超出容差的比较针对足以证明采取行动的变化。跨族计算和合成实验表明，边界交叉支持所提出的修正相对于其参考，但无法唯一识别导致偏移的机制。
英文摘要
A predictive correction is a prespecified modification of an existing predictive distribution intended to reflect an anticipated change in future outcomes given their inputs, motivated, for example, by instrument recalibration, assay drift, or a known intervention. We study how to accumulate anytime-valid evidence that such a correction predicts incoming target outcomes better than the uncorrected source predictive distribution. A fixed nonnegative tilt transforms the source predictive into a corrected predictive, and the corrected-to-source predictive likelihood ratio is a conditional e-value whose running product forms an e-process. This process remains valid under optional stopping and arbitrary input sequences, including adaptively selected ones, while its logarithm equals the cumulative predictive log-score advantage of the correction. A conditional drift decomposition characterizes evidence growth under an arbitrary target predictive distribution, and a correction-dependent half-space identifies misspecified target distributions for which the same false-confirmation bound continues to hold. When the predictive likelihood ratio is strictly positive, its reciprocal yields an anytime-valid refutation boundary, while an overshoot identity explains why the realized null crossing probability may fall below the nominal level. Label-shift, conditional mean and variance, subgroup-specific, and exponential-family corrections arise as special cases. Prespecified mixtures accommodate uncertainty over corrections, predictable tilts permit adaptive betting, and beyond-tolerance comparisons target changes large enough to justify action. Cross-family calculations and synthetic experiments show that a boundary crossing supports the proposed correction relative to its reference but does not uniquely identify the mechanism responsible for the shift.
Comments49 pages
