贝叶斯抽样过程中目标参数的后验不确定性
Posterior Uncertainty for Targeted Parameters in Bayesian Bootstrap Procedures
AI总结：
本文提出了一种广义的链接贝叶斯抽样方法，用于处理贝叶斯抽样中目标参数的后验不确定性，具有良好的频繁性质和可信区间覆盖性。
摘要：
我们提出了一种通用方法，用于在存在有限维干扰参数的情况下对有限维的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。尽管贝叶斯因果推断文献中的大部分研究都依赖于传统的'似然乘以先验'框架，但最近提出的一种方法，即'链接贝叶斯抽样'，偏离了这一经典设定，利用狄利克雷过程和贝叶斯抽样来获得有效的贝叶斯推断。这些方法基于倾向分数的调整，并解释了在研究治疗效应的后验分布时如何处理其不确定性。我们理论上检验了所获得的后验分布的渐近性质，并证明我们提出的方法，即'链接贝叶斯抽样'的广义版本，具有良好的频繁性质。此外，我们还证明可信区间在渐近上具有正确的覆盖性质。我们讨论了我们的方法在因果推断中误设定和单稳健模型中的应用。
英文摘要：
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.
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