## Bernoulli

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

### 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.

#### Article information

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

Dates
Revised: January 2015
First available in Project Euclid: 16 March 2016

https://projecteuclid.org/euclid.bj/1458132996

Digital Object Identifier
doi:10.3150/15-BEJ708

Mathematical Reviews number (MathSciNet)
MR3474830

Zentralblatt MATH identifier
1361.60006

#### Citation

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

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