We defend a new theory of statistical evidence, which we call Robust Bayesianism (RB). We prove that, under widely accepted assumptions, RB entails the law of likelihood [Royall, 1997], the likelihood principle [Berger and Wolpert, 1988], and a variety of other widely-accepted "statistical principles", e.g., the sufficiency principle [Birnbaum, 1962, 1972] and stopping-rule principle [Berger and Wolpert, 1988]. The main technical contribution of this paper is to extend some of those results to a qualitative framework in which experimenters are justified only in making comparative, non-numerical judgments of the form "A given B is more likely than C given D."
翻译:我们捍卫一种新的统计证据理论,我们称之为强势巴伊西亚主义(RB ) 。 我们证明,在广泛接受的假设下,RB包含概率法[Royall,1997年]、概率原则[Berger和Wolpert,1988年]和其他广泛接受的“统计原则”,例如,充足性原则[Birnbaum,1962年,1972年]和停止统治原则[Berger和Wolpert,1988年]。本文的主要技术贡献是将其中一些结果扩展到一个质量框架,实验者只有在对“A给的B比C给的D的可能性更大”的形式作出比较性、非数字性判断时才有理由这样做。