Between the two dominant schools of thought in statistics, namely, Bayesian and classical/frequentist, a main difference is that the former is grounded in the mathematically rigorous theory of probability while the latter is not. In this paper, I show that the latter is grounded in a different but equally mathematically rigorous theory of imprecise probability. Specifically, I show that for every suitable testing or confidence procedure with error rate control guarantees, there exists a consonant plausibility function whose derived testing or confidence procedure is no less efficient. Beyond its foundational implications, this characterization has at least two important practical consequences: first, it simplifies the interpretation of p-values and confidence regions, thus creating opportunities for improved education and scientific communication; second, the constructive proof of the main results leads to a strategy for new and improved methods in challenging inference problems.
翻译:在统计的两个主导思想学派,即巴耶斯学派和古典学派/共产主义学派之间,一个主要区别是前者基于数学上严格的概率理论,而后者则不基于后者。在本文中,我表明后者基于不同但数学上同样严格的概率理论,具体地说,我表明,对于每一个具有错误率控制保证的合适测试或信任程序,都存在着一种兼容的可信任性功能,其衍生的测试或信任程序的效率不亚于前者。除了其基本影响外,这一特征至少具有两个重要的实际后果:首先,它简化了对价值和信任区域的解释,从而为改进教育和科学交流创造了机会;其次,对主要结果的建设性证明导致一项战略,即采用新的和更好的方法来挑战推论问题。