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