We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate low-dimensional functionals of interest without being restricted by the holistic Bayesian formalism. Starting from a conventional nonparametric posterior, we target the functional of interest by transforming the entire distribution with a Bayesian bootstrap correction. We provide conditions for the resulting $\textit{one-step posterior}$ to possess calibrated frequentist properties and specialize the results for several canonical examples: the integrated squared density, the mean of a missing-at-random outcome, and the average causal treatment effect on the treated. The procedure is computationally attractive, requiring only a simple, efficient post-processing step that can be attached onto any arbitrary posterior sampling algorithm. Using the ACIC 2016 causal data analysis competition, we illustrate that our approach can outperform the existing state-of-the-art through the propagation of Bayesian uncertainty.

翻译：我们提出了一种利用修正后验分布进行半参数推断的新方法。该方法能够利用非参数贝叶斯过程的适应性、正则化及预测能力，在不受整体贝叶斯形式主义限制的情况下，估计感兴趣的低维泛函。从常规的非参数后验出发，我们通过贝叶斯自助法修正对整体分布进行变换，从而锁定目标泛函。我们给出了所得$\textit{一步后验}$具有校准频率性质的条件，并将结果具体应用于几个经典示例：积分平方密度、缺失随机结果变量的均值，以及受试者平均因果处理效应。该过程在计算上具有吸引力，仅需一个简单高效的后期处理步骤，可附加于任意后验采样算法。通过2016年ACIC因果数据分析竞赛，我们证明该方法通过传播贝叶斯不确定性，能够超越现有最先进技术。