To improve covariate balance over a complete randomization, a number of methods have been proposed recently to utilize modern computational capabilities to find allocations with balance in observed covariates. Asymptotic inference on treatment effects based on these designs is more complicated than that under complete randomization, and this is why Fisher randomization tests often are suggested. This article suggests model-based Bayesian inference as a general method of inference in these designs, which can deal with complications such as arbitrary covariate balancing criteria and complex estimands. As an illustration, we focus on the case when the outcome is linearly related to the covariates and the estimand of interest is the Sample Average Treatment Effect (SATE). We use a large Monte Carlo simulation to compare the finite sample performance of the model-based Bayesian inference with that of two previous methods which are valid for asymptotic inference of SATE under Mahalanobis distance based rerandomization. We find that for experiments with small to moderate sample sizes, Bayesian inference is to be preferred to the previous methods. As a byproduct, we also find that regression adjustment together with small sample adjusted estimators of standard errors perform better than the previous methods.

中文翻译：

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计算机辅助平衡改进设计下基于模型的贝叶斯推理

为了改善完全随机化的协变量平衡，最近提出了许多方法来利用现代计算能力在观察到的协变量中找到平衡的分配。基于这些设计的治疗效果的渐近推断比完全随机化下的更复杂，这就是为什么经常建议使用 Fisher 随机化检验的原因。本文建议将基于模型的贝叶斯推理作为这些设计中的一种通用推理方法，它可以处理任意协变量平衡标准和复杂估计等复杂问题。作为说明，我们关注结果与协变量线性相关并且感兴趣的估计是样本平均治疗效果（SATE）的情况。我们使用大型蒙特卡罗模拟来比较基于模型的贝叶斯推理的有限样本性能与之前两种方法的有限样本性能，这两种方法在基于马氏距离的重随机化下对 SATE 的渐近推理有效。我们发现，对于小到中等样本量的实验，贝叶斯推理比以前的方法更受欢迎。作为副产品，我们还发现回归调整与小样本调整的标准误差估计器一起执行比以前的方法更好。