We provide a simple and general solution to the fundamental open problem of inaccurate uncertainty quantification of Bayesian inference in misspecified or approximate models, and of generalized Bayesian posteriors more generally. While existing solutions are based on explicit Gaussian posterior approximations, or computationally onerous post-processing procedures, we demonstrate that correct uncertainty quantification can be achieved by substituting the usual posterior with an alternative posterior that conveys the same information. This solution applies to both likelihood-based and loss-based posteriors, and we formally demonstrate the reliable uncertainty quantification of this approach. The new approach is demonstrated through a range of examples, including generalized linear models, and doubly intractable models.

翻译：我们针对贝叶斯推断在模型误设定或近似模型下不确定性量化不准确这一基础开放问题，以及更广义的贝叶斯后验分布中的同类问题，提出了一种简洁且通用的解决方案。现有方法要么依赖显式高斯后验近似，要么依赖计算代价高昂的后处理程序，而我们证明，通过用传达相同信息的替代后验分布替换常规后验分布，即可实现正确的不确定性量化。该方案同时适用于基于似然函数和基于损失函数的后验分布，我们严格论证了该方法在不确定性量化上的可靠性。通过广义线性模型和双重难解模型等一系列示例，本文展示了该新方法的有效性。