Open Access
August 2016 Approximation of improper priors
Christele Bioche, Pierre Druilhet
Bernoulli 22(3): 1709-1728 (August 2016). DOI: 10.3150/15-BEJ708


We propose a convergence mode for positive Radon measures which allows a sequence of probability measures to have an improper limiting measure. We define a sequence of vague priors as a sequence of probability measures that converges to an improper prior. We consider some cases where vague priors have necessarily large variances and other cases where they have not. We study the consequences of the convergence of prior distributions on the posterior analysis. Then we give some constructions of vague priors that approximate the Haar measures or the Jeffreys priors. We also revisit the Jeffreys–Lindley paradox.


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Christele Bioche. Pierre Druilhet. "Approximation of improper priors." Bernoulli 22 (3) 1709 - 1728, August 2016.


Received: 1 July 2014; Revised: 1 January 2015; Published: August 2016
First available in Project Euclid: 16 March 2016

zbMATH: 1361.60006
MathSciNet: MR3474830
Digital Object Identifier: 10.3150/15-BEJ708

Keywords: approximation of improper priors , conjugate priors , convergence of prior , Jeffreys–Lindley paradox , non-informative priors , the Jeffreys prior , vague priors

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 3 • August 2016
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