Open Access
April 2009 The formal definition of reference priors
James O. Berger, José M. Bernardo, Dongchu Sun
Ann. Statist. 37(2): 905-938 (April 2009). DOI: 10.1214/07-AOS587


Reference analysis produces objective Bayesian inference, in the sense that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a certain information-theoretic sense. Reference priors have been rigorously defined in specific contexts and heuristically defined in general, but a rigorous general definition has been lacking. We produce a rigorous general definition here and then show how an explicit expression for the reference prior can be obtained under very weak regularity conditions. The explicit expression can be used to derive new reference priors both analytically and numerically.


Download Citation

James O. Berger. José M. Bernardo. Dongchu Sun. "The formal definition of reference priors." Ann. Statist. 37 (2) 905 - 938, April 2009.


Published: April 2009
First available in Project Euclid: 10 March 2009

zbMATH: 1162.62013
MathSciNet: MR2502655
Digital Object Identifier: 10.1214/07-AOS587

Primary: 62F15
Secondary: 62A01 , 62B10

Keywords: Amount of information , Bayesian asymptotics , consensus priors , Fisher information , Jeffreys priors , noninformative priors , objective priors , reference priors

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 2 • April 2009
Back to Top