  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.
