标题： 通过后验耦合的贝叶斯双重稳健因果推断 显示英文标题

标题： Bayesian Doubly Robust Causal Inference via Posterior Coupling

摘要： 贝叶斯双重稳健（DR）因果推断面临一个根本性困境：联合建模结果和倾向得分会遇到反馈问题，其中结果信息污染了倾向得分估计，而两步分析则为了计算便利性牺牲了有效的后验分布。我们通过熵倾斜的后验耦合解决了这一困境。我们的框架为倾向得分和结果模型构建独立的后验分布，然后使用熵倾斜将它们耦合以强制DR矩条件。这产生了第一个具有显式后验分布的完全贝叶斯DR估计器。理论上，我们建立了三个关键属性：(i) 当结果模型正确指定时，倾斜后的后验与原始后验一致；(ii) 在倾向得分模型正确的情况下，即使结果模型错误指定，后验均值仍保持一致；(iii) 非参数结果模型的收敛速度得到改善。模拟结果显示，与现有方法相比，偏差减少和效率更高。我们通过两个应用展示了所提出方法的实际优势：抗高血压治疗对痴呆影响中未测量混杂因素的敏感性分析，以及结合收缩先验和修改矩条件的右心导管术死亡率高维混杂因素选择。我们提供了一个实现所提出方法的R包。 显示英文摘要

摘要： Bayesian doubly robust (DR) causal inference faces a fundamental dilemma: joint modeling of outcome and propensity score suffers from the feedback problem where outcome information contaminates propensity score estimation, while two-step analysis sacrifices valid posterior distributions for computational convenience. We resolve this dilemma through posterior coupling via entropic tilting. Our framework constructs independent posteriors for propensity score and outcome models, then couples them using entropic tilting to enforce the DR moment condition. This yields the first fully Bayesian DR estimator with an explicit posterior distribution. Theoretically, we establish three key properties: (i) when the outcome model is correctly specified, the tilted posterior coincides with the original; (ii) under propensity score model correctness, the posterior mean remains consistent despite outcome model misspecification; (iii) convergence rates improve for nonparametric outcome models. Simulations demonstrate superior bias reduction and efficiency compared to existing methods. We illustrate practical advantages of the proposed method through two applications: sensitivity analysis for unmeasured confounding in antihypertensive treatment effects on dementia, and high-dimensional confounder selection combining shrinkage priors with modified moment conditions for right heart catheterization mortality. We provide an R package implementing the proposed method.