We propose a simple approach that provides accurate uncertainty quantification for Bayesian inference in misspecified or approximate models, and for generalized (Gibbs) posteriors. While existing solutions in this context are based on explicit Gaussian approximations or post-processing procedures, we demonstrate that correct uncertainty quantification can be achieved by substituting the usual posterior with an intuitively appealing alternative that conveys the same information. This solution applies to both likelihood-based and loss-based posteriors, and is formally demonstrated to reliably quantify uncertainty. This new approach is demonstrated through a range of examples, including generalized linear models, and doubly intractable models.

翻译：本文提出一种简洁方法，可为错误设定或近似模型中的贝叶斯推断以及广义（吉布斯）后验提供精确的不确定性量化。尽管该领域现有解决方案基于显式高斯近似或后处理流程，但我们证明通过将常规后验替换为传达相同信息且直观合理的替代形式，即可实现正确的不确定性量化。该解决方案适用于基于似然函数和基于损失函数的后验分布，并经过形式化证明能够可靠地量化不确定性。我们通过包括广义线性模型和双重难处理模型在内的一系列示例，验证了这种新方法的有效性。