标题： 使用反事实逻辑恢复具有选择偏差的实验数据 显示英文标题

标题： Recover Experimental Data with Selection Bias using Counterfactual Logic

摘要： 选择偏差，即由于系统性地包含或排除某些样本而产生，对因果推理的有效性构成了重大挑战。 尽管Bareinboim等人引入了从有偏数据中利用部分外部信息恢复无偏观测和干预分布的方法，但后门调整的复杂性以及该方法对观测数据的强烈依赖限制了它在许多实际场景中的适用性。 本文正式探讨了在选择偏差下通过实验数据恢复$P(Y^*_{x^*})$的可能性。 通过显式构建结构因果模型（SCMs）中的反事实世界，我们分析了观测世界中的选择机制如何传播到反事实领域。 我们推导出一组完整的图形和理论标准，以确定实验分布是否受选择偏差影响。 此外，我们提出了原则性的方法，利用部分无偏的观测数据从有偏的实验数据集中恢复$P(Y^*_{x^*})$。 模拟研究复制了现实的研究情景，展示了我们方法的实际效用，为缓解应用因果推理中的选择偏差提供了具体的指导。 显示英文摘要

摘要： Selection bias, arising from the systematic inclusion or exclusion of certain samples, poses a significant challenge to the validity of causal inference. While Bareinboim et al. introduced methods for recovering unbiased observational and interventional distributions from biased data using partial external information, the complexity of the backdoor adjustment and the method's strong reliance on observational data limit its applicability in many practical settings. In this paper, we formally discover the recoverability of $P(Y^*_{x^*})$ under selection bias with experimental data. By explicitly constructing counterfactual worlds via Structural Causal Models (SCMs), we analyze how selection mechanisms in the observational world propagate to the counterfactual domain. We derive a complete set of graphical and theoretical criteria to determine that the experimental distribution remain unaffected by selection bias. Furthermore, we propose principled methods for leveraging partially unbiased observational data to recover $P(Y^*_{x^*})$ from biased experimental datasets. Simulation studies replicating realistic research scenarios demonstrate the practical utility of our approach, offering concrete guidance for mitigating selection bias in applied causal inference.