Re-randomization has gained popularity as a tool for experiment-based causal inference due to its superior covariate balance and statistical efficiency compared to classic randomized experiments. However, the basic re-randomization method, known as ReM, and many of its extensions have been deemed sub-optimal as they fail to prioritize covariates that are more strongly associated with potential outcomes. To address this limitation and design more efficient re-randomization procedures, a more precise quantification of covariate heterogeneity and its impact on the causal effect estimator is in a great appeal. This work fills in this gap with a Bayesian criterion for re-randomization and a series of novel re-randomization procedures derived under such a criterion. Both theoretical analyses and numerical studies show that the proposed re-randomization procedures under the Bayesian criterion outperform existing ReM-based procedures significantly in effectively balancing covariates and precisely estimating the unknown causal effect.

翻译：重随机化作为一种基于实验的因果推断工具，因其优于经典随机化实验的协变量平衡性和统计效率而日益受到青睐。然而，基础重随机化方法ReM及其诸多扩展方法因未能优先处理与潜在结果关联更强的协变量，已被认为存在次优性。为解决这一局限并设计更高效的重随机化程序，亟需对协变量异质性及其对因果效应估计量的影响进行更精确的量化。本研究通过提出贝叶斯重随机化准则及由此导出的系列新型重随机化程序填补了这一空白。理论分析与数值研究均表明，在贝叶斯准则下提出的重随机化程序在有效平衡协变量与精准估计未知因果效应方面显著优于现有基于ReM的方法。