- Volume 22, Number 3 (2016), 1709-1728.
Approximation of improper priors
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.
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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Bioche, Christele; Druilhet, Pierre. Approximation of improper priors. Bernoulli 22 (2016), no. 3, 1709--1728. doi:10.3150/15-BEJ708. https://projecteuclid.org/euclid.bj/1458132996