Frequentist inference has a well-established supporting theory for doubly robust causal inference based on the potential outcomes framework, which is realized via outcome regression (OR) and propensity score (PS) models. The Bayesian counterpart, however, is not obvious as the PS model loses its balancing property in joint modeling. In this paper, we propose a natural and formal Bayesian solution by bridging loss-type Bayesian inference with a utility function derived from the notion of a pseudo-population via the change of measure. Consistency of the posterior distribution is shown with correctly specified and misspecified OR models. Simulation studies suggest that our proposed method can estimate the true causal effect more efficiently and achieve the frequentist coverage if either the OR model is correctly specified or fit with a flexible function of the confounders, compared to the previous Bayesian approach via the Bayesian bootstrap. Finally, we apply this novel Bayesian method to assess the impact of speed cameras on the reduction of car collisions in England.
翻译:常见的推论有一个基于潜在结果框架的双重稳健因果推论的既定支持理论,这种推论是通过结果回归(OR)和倾向性评分(PS)模型实现的。然而,巴伊西亚对应方并不明显,因为PS模型在联合建模中失去了平衡属性。在本文中,我们提出一种自然和正式的巴伊西亚解决办法,办法是弥补损失类型巴伊西亚的推论,这种推论具有因改变计量方法而衍生的伪人口概念的实用功能。后方分布的一致性以正确指定和错误的OR模型显示。模拟研究表明,如果与先前的巴伊西亚方法相比,或者正确指定了OR模型,或者与交错者的灵活功能相匹配,那么我们提出的方法可以更高效地估计真正的因果效应并实现常态覆盖。最后,我们采用这种新型的巴伊西亚方法来评估高速摄像头对减少英格兰汽车碰撞的影响。