• Bernoulli
  • Volume 22, Number 3 (2016), 1709-1728.

Approximation of improper priors

Christele Bioche and Pierre Druilhet

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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.

Article information

Bernoulli, Volume 22, Number 3 (2016), 1709-1728.

Received: July 2014
Revised: January 2015
First available in Project Euclid: 16 March 2016

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


Bioche, Christele; Druilhet, Pierre. Approximation of improper priors. Bernoulli 22 (2016), no. 3, 1709--1728. doi:10.3150/15-BEJ708.

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