The Annals of Statistics

Objective priors for the bivariate normal model

James O. Berger and Dongchu Sun

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 13 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1205420525

Digital Object Identifier
doi:10.1214/07-AOS501

Mathematical Reviews number (MathSciNet)
MR2396821

Zentralblatt MATH identifier
1133.62014

Subjects
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.)

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

Citation

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. https://projecteuclid.org/euclid.aos/1205420525


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