Bayesian Analysis
- Bayesian Anal.
- Volume 7, Number 4 (2012), 903-916.
Invariant Conjugate Analysis for Exponential Families
Pierre Druilhet and Denys Pommeret
Abstract
There are several ways to parameterize a distribution belonging to an exponential family, each one leading to a different Bayesian analysis of the data under standard conjugate priors. To overcome this problem, we propose a new class of conjugate priors which is invariant with respect to smooth reparameterization. This class of priors contains the Jeffreys prior as a special case, according to the value of the hyperparameters. Moreover, these conjugate distributions coincide with the posterior distributions resulting from a Jeffreys prior. Then these priors appear naturally when several datasets are analyzed sequentially and when the Jeffreys prior is chosen for the first dataset. We apply our approach to inverse Gaussian models and propose full invariant analyses of three datasets.
Article information
Source
Bayesian Anal., Volume 7, Number 4 (2012), 903-916.
Dates
First available in Project Euclid: 27 November 2012
Permanent link to this document
https://projecteuclid.org/euclid.ba/1354024467
Digital Object Identifier
doi:10.1214/12-BA731
Mathematical Reviews number (MathSciNet)
MR3000019
Zentralblatt MATH identifier
1330.62119
Keywords
Bayesian inference conjugate prior exponential family inverse Gaussian distribution Jeffreys prior sequential analysis
Citation
Druilhet, Pierre; Pommeret, Denys. Invariant Conjugate Analysis for Exponential Families. Bayesian Anal. 7 (2012), no. 4, 903--916. doi:10.1214/12-BA731. https://projecteuclid.org/euclid.ba/1354024467