We study Bayesian approaches to causal inference via propensity score regression. Much of the Bayesian literature on propensity score methods have relied on approaches that cannot be viewed as fully Bayesian in the context of conventional `likelihood times prior' posterior inference; in addition, most methods rely on parametric and distributional assumptions, and presumed correct specification. We emphasize that causal inference is typically carried out in settings of mis-specification, and develop strategies for fully Bayesian inference that reflect this. We focus on methods based on decision-theoretic arguments, and show how inference based on loss-minimization can give valid and fully Bayesian inference. We propose a computational approach to inference based on the Bayesian bootstrap which has good Bayesian and frequentist properties.

翻译：我们研究了贝叶斯人通过偏好分数回归来进行因果关系推断的方法,巴伊斯人关于偏好分分数方法的许多文献都依赖在传统的`先前的相似时间'后继推论中不能被视为完全巴伊斯人的方法;此外,大多数方法都依赖于参数和分布假设,并假定正确的规格;我们强调,因果关系推断通常是在具体错误的情况下进行的,我们注重基于决定理论论的推论方法,并表明基于损失最小化的推论如何能提供有效和完全巴伊斯人的推论;我们建议一种基于巴伊斯人长靴子的推论计算方法,因为巴伊斯长靴子具有良好的巴伊斯人和常客特性。