Bayesian inference provides a framework to combine various model components with shared parameters, allowing joint uncertainty estimation and the use of all available data sources. Unfortunately, misspecification of any part of the model might propagate to all other parts and can lead to unsatisfactory results. Cut distributions have been proposed as a remedy, where the information is prevented from flowing along certain directions. We study cut distributions from an asymptotic perspective and obtain a Bernstein-von Mises theorem, as well as a Laplace approximation with quantitative bounds. We then propose an algorithm based on the Posterior Bootstrap that delivers credible regions with the nominal frequentist asymptotic coverage. The proposed methods are illustrated with numerical experiments in a variety of examples, including causal inference with propensity scores.

翻译：贝叶斯推断为整合具有共享参数的不同模型组件提供了框架，使得能够进行联合不确定性估计并利用所有可用数据源。然而，模型中任何部分的误设都可能传播至其他所有部分，导致不理想的结果。割分布被提出作为一种解决方案，通过阻止信息沿特定方向传递来缓解此问题。本文从渐近视角研究割分布，获得了Bernstein-von Mises定理以及带有定量界限的拉普拉斯近似。随后，我们提出一种基于后验自助法的算法，该算法能够提供具有名义频率派渐近覆盖度的可信区域。所提方法通过多种数值实验案例得到验证，包括基于倾向得分的因果推断研究。