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April 2008 Objective priors for the bivariate normal model
James O. Berger, Dongchu Sun
Ann. Statist. 36(2): 963-982 (April 2008). DOI: 10.1214/07-AOS501

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.

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James O. Berger. Dongchu Sun. "Objective priors for the bivariate normal model." Ann. Statist. 36 (2) 963 - 982, April 2008. https://doi.org/10.1214/07-AOS501

Information

Published: April 2008
First available in Project Euclid: 13 March 2008

zbMATH: 1133.62014
MathSciNet: MR2396821
Digital Object Identifier: 10.1214/07-AOS501

Subjects:
Primary: 62F10 , 62F15 , 62F25
Secondary: 62A01 , 62E15 , 62H10 , 62H20

Keywords: constructive posterior distributions , Fiducial inference , frequentist coverage , Jeffreys priors , marginalization paradox , matching priors , reference priors , rejection sampling , right-Haar prior

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 2 • April 2008
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