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 is generalised to widen the range of frequentist applications of posterior convergence. With Bayesian tests and a weakened form of contiguity termed remote contiguity, we prove simple and fully general frequentist theorems, for posterior consistency and rates of convergence, for consistency of posterior odds in model selection, and for conversion of sequences of credible sets into sequences of confidence sets with asymptotic coverage one. For frequentist uncertainty quantification, this means that a prior inducing remote contiguity allows one to enlarge credible sets of calculated, simulated or approximated posteriors to obtain asymptotically consistent confidence sets.

中文翻译：

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贝叶斯极限的频繁有效性

对于计算后验的常客来说，并不是所有先验都可以渐近地使用：在本文中，提出了贝叶斯关于测试序列的观点，并且推广了Schwartz的Kullback-Leibler条件，以扩大后验收敛的常客应用范围。使用贝叶斯测试和弱化的连续性称为远程连续性，我们证明了简单和完全通用的常驻性定理，用于后验一致性和收敛速度，用于模型选择中的后验优势一致性，以及用于将可信集的序列转换为渐近覆盖为1的置信集的序列。对于频繁不确定性量化，这意味着先验诱发远程连续性可以扩大计算，模拟或近似后验的可信集，以获得渐近一致的置信集。