Annals of Statistics

The formal definition of reference priors

James O. Berger, José M. Bernardo, and Dongchu Sun

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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.

Article information

Ann. Statist., Volume 37, Number 2 (2009), 905-938.

First available in Project Euclid: 10 March 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F15: Bayesian inference
Secondary: 62A01: Foundations and philosophical topics 62B10: Information-theoretic topics [See also 94A17]

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


Berger, James O.; Bernardo, José M.; Sun, Dongchu. The formal definition of reference priors. Ann. Statist. 37 (2009), no. 2, 905--938. doi:10.1214/07-AOS587.

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