On the mathematics of the Jeffreys–Lindley paradox |
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Authors: | Cristiano Villa Stephen Walker |
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Institution: | 1. University of Kent, School of Mathematics, Statistics and Actuarial Sciences, Cornwallis Building, University of Kent, Canterbury, UK;2. Department of Mathematics, University of Texas at Austin, Austin, TX, USA |
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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. |
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Keywords: | Bayes factor Bayesian hypothesis testing Kullback–Leibler divergence self-information loss |
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