The Annals of Statistics

Objective priors for the bivariate normal model

James O. Berger and Dongchu Sun

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Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of inference (e.g., Bayesian, frequentist, fiducial) and the criteria involved in deciding on optimal objective priors (e.g., ease of computation, frequentist performance, marginalization paradoxes). Summary recommendations as to optimal objective priors are made for a variety of inferences involving the bivariate normal distribution.

In the course of the investigation, a variety of surprising results were found, including the availability of objective priors that yield exact frequentist inferences for many functions of the bivariate normal parameters, including the correlation coefficient.

Article information

Ann. Statist., Volume 36, Number 2 (2008), 963-982.

First available in Project Euclid: 13 March 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F10: Point estimation 62F15: Bayesian inference 62F25: Tolerance and confidence regions
Secondary: 62A01: Foundations and philosophical topics 62E15: Exact distribution theory 62H10: Distribution of statistics 62H20: Measures of association (correlation, canonical correlation, etc.)

Reference priors matching priors Jeffreys priors right-Haar prior fiducial inference frequentist coverage marginalization paradox rejection sampling constructive posterior distributions


Berger, James O.; Sun, Dongchu. Objective priors for the bivariate normal model. Ann. Statist. 36 (2008), no. 2, 963--982. doi:10.1214/07-AOS501.

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