Frequentist validity of Bayesian limits

To the frequentist who computes posteriors, not all priors are useful asymptotically: in this paper, a Bayesian perspective on test sequences is proposed and Schwartz’s Kullback–Leibler condition generalised to widen range of applications posterior convergence. With tests weakened form contiguity termed remote contiguity, we prove simple fully general theorems, for consistency rates convergence, odds model selection, conversion credible sets into confidence with asymptotic coverage one. For uncertainty quantification, means that prior inducing allows one enlarge calculated, simulated or approximated posteriors obtain asymptotically consistent sets.