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.

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