We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker common-sense criteria for solutions to inference problems, all failed by these frequentist methods but satisfied by any admissible method. We note that pseudo-Bayesian methods made by handicapping Bayesian methods to satisfy criteria on type I error rate makes them frequentist not Bayesian in nature. We give five examples showing the differences between Bayesian and frequentist methods; the first requiring little calculus, the second showing in abstract what is wrong with these frequentist methods, the third to illustrate information conservation, the fourth to show that the same problems arise in everyday statistical problems, and the fifth to illustrate how on some real-life inference problems Bayesian methods require less data than fixed sample-size (resp. pseudo-Bayesian) frequentist hypothesis testing by factors exceeding 3000 (resp 300) without recourse to informative priors. To address the issue of different parties with opposing interests reaching agreement on a prior, we illustrate the beneficial effects of a Bayesian "Let the data decide" policy both on results under a wide variety of conditions and on motivation to reach a common prior by consent. We show that in general the frequentist confidence level contains less relevant Shannon information than the Bayesian posterior, and give an example where no deterministic frequentist critical regions give any relevant information even though the Bayesian posterior contains up to the maximum possible amount. In contrast use of the Bayesian prior allows construction of non-deterministic critical regions for which the Bayesian posterior can be recovered from the frequentist confidence.

翻译：我们列举了支持贝叶斯假设检验与置信集合优于频率学派方法的论据。定义了推断问题的可容许解，并指出贝叶斯解具有可容许性。给出了七个较弱的常理准则用于评估推断问题解，频率学派方法均未通过，而任何可容许性方法均满足。指出通过削弱贝叶斯方法以满足第一类错误率准则所构建的伪贝叶斯方法，本质上属于频率学派而非贝叶斯方法。通过五个实例展现贝叶斯与频率学派方法的差异：第一个仅需初等微积分，第二个从抽象角度揭示频率学派方法的缺陷，第三个阐释信息守恒原理，第四个证明相同问题在常规统计中普遍存在，第五个展示在现实推断问题中，贝叶斯方法所需数据量比固定样本量（或伪贝叶斯）频率学派假设检验分别少3000倍和300倍，且无需引入信息性先验。针对利益相左各方就先验达成一致的问题，通过贝叶斯"让数据决策"策略的利好效应进行阐释，该效应既体现在广泛条件下产生的结果中，也体现在促使各方自愿协商共同先验的动机上。我们证明频率学派置信水平所含香农信息通常少于贝叶斯后验，并给出实例：当贝叶斯后验包含最大可能信息量时，确定性频率学派临界区域却无法提供任何有效信息。相反，利用贝叶斯先验可构建非确定性临界区域，使得频率学派置信区间能够还原贝叶斯后验信息。