Approximation of improper priors
Abstract
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.
Cite
@article{arxiv.1311.1067,
title = {Approximation of improper priors},
author = {Christele Bioche and Pierre Druilhet},
journal= {arXiv preprint arXiv:1311.1067},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.3150/15-BEJ708 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)