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

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An Erratum to this article was published on 19 February 2015

Abstract

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.

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Acknowledgments

I thank my colleagues in high energy physics, and in the CMS collaboration in particular, for many useful discussions. I am grateful to members of the CMS Statistics Committee, for comments on an early draft of the manuscript, and in particular to Luc Demortier and Louis Lyons for continued discussions. Tom Ferbel provided invaluable detailed comments on two previous versions that I posted on the arXiv. The PhyStat series of workshops organized by Louis Lyons has led to many fruitful discussions and enlightening contact with prominent members of the statistics community. This material is based upon work partially supported by the U.S. Department of Energy under Award Number DE-SC0009937.

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    Robert D. Cousins

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Cousins, R.D. The Jeffreys–Lindley paradox and discovery criteria in high energy physics. Synthese 194, 395–432 (2017). https://doi.org/10.1007/s11229-014-0525-z

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