# On The Mathematics of The Jeffreys-Lindley Paradox

Villa, Cristiano, Walker, Stephen G. (2017) On The Mathematics of The Jeffreys-Lindley Paradox. Communications in Statistics – Theory and Methods, 46 (24). pp. 12290-12298. ISSN 0361-0926. (doi:10.1080/03610926.2017.1295073)

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http://dx.doi.org/10.1080/03610926.2017.1295073

## Abstract

This paper is concerned with the well known Jeffreys-Lindley paradox. In a Bayesian set up, the so-called paradox arises when a point null hypothesis is tested and an objective prior is sought for the alternative hypothesis. In particular, the posterior for the null hypothesis tends to one when the uncertainty, i.e. the variance, for the parameter value goes to infinity. We argue that the appropriate way to deal with the paradox is to use simple mathematics, and that any philosophical argument is to be regarded as irrelevant.

Item Type: Article 10.1080/03610926.2017.1295073 Bayes factor, Bayesian hypothesis testing, Kullback–Leibler divergence, self-information loss Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics Cristiano Villa 08 Feb 2017 08:37 UTC 11 Jul 2019 13:39 UTC https://kar.kent.ac.uk/id/eprint/60238 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-2670-2954