Although propensity scores have been central to the estimation of causal effects for over 30 years, only recently has the statistical literature begun to consider in detail methods for Bayesian estimation of propensity scores and causal effects. Underlying this recent body of literature on Bayesian propensity score estimation is an implicit discordance between the goal of the propensity score and the use of Bayes’ theorem. The propensity score condenses multivariate covariate information into a scalar to allow estimation of causal effects without specifying a model for how each covariate relates to the outcome. Avoiding specification of a detailed model for the outcome response surface is valuable for robust estimation of causal effects, but this strategy is at odds with the use of Bayes’ theorem, which presupposes a full probability model for the observed data that adheres to the likelihood principle. The goal of this article is to explicate this fundamental feature of Bayesian estimation of causal effects with propensity scores to provide context for the existing literature and for future work on this important topic. [Received June 2014. Revised September 2015.]

中文翻译：

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贝叶斯定理在因果效应和倾向得分联合估计中的核心作用

尽管 30 多年来，倾向评分一直是因果效应估计的核心，但直到最近，统计文献才开始详细考虑贝叶斯估计倾向评分和因果效应的方法。在最近有关贝叶斯倾向得分估计的大量文献的基础上，倾向得分的目标与贝叶斯定理的使用之间存在隐含的不一致。倾向得分将多元协变量信息浓缩为一个标量，以允许估计因果效应，而无需指定每个协变量如何与结果相关的模型。避免为结果响应面指定详细模型对于因果效应的稳健估计是有价值的，但这种策略与贝叶斯定理的使用不一致，它预设了遵守似然原理的观测数据的全概率模型。本文的目的是用倾向得分来解释贝叶斯因果效应估计的这一基本特征，为现有文献和这一重要主题的未来工作提供背景。[2014 年 6 月收到。2015 年 9 月修订。]