中文摘要
我们提出了一种在无混淆性假设下对平均处理效应（ATE）进行双重稳健贝叶斯推断的方法。在这一新的贝叶斯方法中，我们首先调整条件均值函数的先验分布，然后修正由此得到的 ATE 后验分布。这两项调整均利用了受 ATE 估计的半参数影响函数启发的预估计量。我们通过在双重稳健性条件下建立一个新的半参数 Bernstein–von Mises 定理，证明了本文贝叶斯方法与有效频率学派 ATE 估计量之间的渐近等价性；也就是说，条件均值函数光滑性的不足可由倾向得分的高正则性加以补偿，反之亦然。因此，所得贝叶斯可信集构成了具有渐近精确覆盖概率的置信区间。在模拟中，我们的方法通过后验均值给出了精确的 ATE 点估计，其可信区间也与名义覆盖概率高度吻合。此外，与现有方法相比，本文方法所得区间长度更短。我们参照 LaLonde（1986）以及 Dehejia 和 Wahba（1999），将该方法应用于国家支持工作示范项目，以说明其实际效果。
Abstract
We propose a double robust Bayesian inference procedure on the average treatment effect (ATE) under unconfoundedness. For our new Bayesian approach, we first adjust the prior distributions of the conditional mean functions, and then correct the posterior distribution of the resulting ATE. Both adjustments make use of pilot estimators motivated by the semiparametric influence function for ATE estimation. We prove asymptotic equivalence of our Bayesian procedure and efficient frequentist ATE estimators by establishing a new semiparametric Bernstein–von Mises theorem under double robustness; that is, the lack of smoothness of conditional mean functions can be compensated by high regularity of the propensity score and vice versa. Consequently, the resulting Bayesian credible sets form confidence intervals with asymptotically exact coverage probability. In simulations, our method provides precise point estimates of the ATE through the posterior mean and delivers credible intervals that closely align with the nominal coverage probability. Furthermore, our approach achieves a shorter interval length in comparison to existing methods. We illustrate our method in an application to the National Supported Work Demonstration following LaLonde (1986) and Dehejia and Wahba (1999).