标题： 目标参数的后验不确定性在贝叶斯Bootstrap过程中 显示英文标题

标题： Posterior Uncertainty for Targeted Parameters in Bayesian Bootstrap Procedures

摘要： 我们提出了一种通用方法，在存在有限维干扰参数的情况下，对有限维“目标”参数进行有效的贝叶斯分析。 我们将我们的方法应用于基于估计方程的因果推断。 虽然贝叶斯因果推断领域的大部分文献都依赖于传统的“似然乘以先验”框架，但一种最近提出的“链接贝叶斯引导法”偏离了这一经典设置，通过使用狄利克雷过程和贝叶斯引导法获得了有效的贝叶斯推断。 这些方法基于倾向得分的调整，并解释了在研究处理效应后验分布时如何处理其不确定性。 我们从理论上考察了所得后验分布的渐近性质，并表明我们提出的这种方法，即“链接贝叶斯引导法”的广义版本，具有理想的频率学性质。 此外，我们证明了可信区间具有渐近正确的覆盖性质。 我们讨论了我们的方法在因果推断中误设定和单一致模型中的应用。 显示英文摘要

摘要： We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating equations. While much of the literature in Bayesian causal inference has relied on the conventional 'likelihood times prior' framework, a recently proposed method, the 'Linked Bayesian Bootstrap', deviated from this classical setting to obtain valid Bayesian inference using the Dirichlet process and the Bayesian bootstrap. These methods rely on an adjustment based on the propensity score and explain how to handle the uncertainty concerning it when studying the posterior distribution of a treatment effect. We examine theoretically the asymptotic properties of the posterior distribution obtained and show that our proposed method, a generalized version of the 'Linked Bayesian Bootstrap', enjoys desirable frequentist properties. In addition, we show that the credible intervals have asymptotically the correct coverage properties. We discuss the applications of our method to mis-specified and singly-robust models in causal inference.