The Jeffreys–Lindley paradox and discovery criteria in high energy physics

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• 作者：Robert D. Cousins
• 关键词：Jeffreys–Lindley paradox ; Lindley’s paradox ; Bayesian model selection ; p values ; High energy physics
• 刊名：Synthese
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：194
• 期：2
• 页码：395-432
• 全文大小：
• 刊物类别：Humanities, Social Sciences and Law
• 刊物主题：Philosophy of Science; Epistemology; Logic; Philosophy of Language; Metaphysics;
• 出版者：Springer Netherlands
• ISSN：1573-0964
• 卷排序：194

文摘

The Jeffreys–Lindley paradox displays how the use of a \(p\) value (or number of standard deviations \(z\)) in a frequentist hypothesis test can lead to an inference that is radically different from that of a Bayesian hypothesis test in the form advocated by Harold Jeffreys in the 1930s and common today. The setting is the test of a well-specified null hypothesis (such as the Standard Model of elementary particle physics, possibly with “nuisance parameters”) versus a composite alternative (such as the Standard Model plus a new force of nature of unknown strength). The \(p\) value, as well as the ratio of the likelihood under the null hypothesis to the maximized likelihood under the alternative, can strongly disfavor the null hypothesis, while the Bayesian posterior probability for the null hypothesis can be arbitrarily large. The academic statistics literature contains many impassioned comments on this paradox, yet there is no consensus either on its relevance to scientific communication or on its correct resolution. The paradox is quite relevant to frontier research in high energy physics. This paper is an attempt to explain the situation to both physicists and statisticians, in the hope that further progress can be made.