半参数贝叶斯模型中的自助法有效性
Bootstrap validity in Bayesian semi-parametric models
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中文总结 AI 辅助
该研究在半参数贝叶斯推断框架下，结合Dirichlet过程与贝叶斯自助法，放宽随机等连续性假设，验证了后验分布的渐近正态性与收敛性，并通过模拟确认了分析结果。
中文摘要 AI 辅助
我们在半参数推断框架下，采用估计函数方法，探讨了在可能存在高度复杂的冗余成分时，对低维目标参数进行贝叶斯推断的问题。我们通过Dirichlet过程（一种非参数贝叶斯方法）和贝叶斯自助法获得后验分布。我们放宽了常用的随机等连续性概念，构建了一个能产生具有良好频率性质的后验推断的框架，具体而言，我们证明该后验分布渐近正态，且会收敛到参数的真实值。我们强调获得这些结果所需的特定假设，以及放宽其中任何一个假设如何改变结论。我们通过模拟验证了分析结果。
英文摘要
We discuss Bayesian inference on a low-dimensional targeted parameter in the presence of possibly highly complex nuisance components within the semi-parametric inference framework using an estimating function approach. We obtain a posterior distribution using non-parametric Bayesian methods through the Dirichlet process and the Bayesian bootstrap. We relax the commonly deployed notion of stochastic equicontinuity and develop a framework leading to posterior inference with good frequentist properties, specifically we demonstrate that the posterior distribution is asymptotically Normal and concentrates at the true value of the parameter. We emphasize the specific assumptions that are required to obtain these results, and how relaxing any of them alters the conclusions. We verify the analytical results in simulation.
