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December, 1990 Reference Priors for the Orbit in a Group Model
Ted Chang, David Eaves
Ann. Statist. 18(4): 1595-1614 (December, 1990). DOI: 10.1214/aos/1176347868


For a group model in which the group $\mathbf{G}$ acts freely on the parameter space $\mathbf{\Omega}$, this paper considers a prior which is a product of right Haar measure on $\mathbf{G}$ and a limiting form of Jeffreys' prior for the maximal invariant. When the parameter of interest is the orbit of $\mathbf{G}$ in $\mathbf{\Omega}$, it is shown that such a prior is the reference prior defined by Bernardo. A method of calculating this reference prior is given which avoids the necessity of working in a parameterization of $\mathbf{\Omega}$ which expresses $\mathbf{\Omega}$ as a product of $\mathbf{G}$ and a cross section. Examples of the multivariate normal distribution, with the parameter of interest being the correlation matrix or the eigenvalues of the covariance matrix, are discussed.


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Ted Chang. David Eaves. "Reference Priors for the Orbit in a Group Model." Ann. Statist. 18 (4) 1595 - 1614, December, 1990.


Published: December, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0725.62003
MathSciNet: MR1074425
Digital Object Identifier: 10.1214/aos/1176347868

Primary: 62A05
Secondary: 62F15 , 62H20 , 62H25

Keywords: Bayesian inference in group models , maximal invariant , noninformative priors

Rights: Copyright © 1990 Institute of Mathematical Statistics


Vol.18 • No. 4 • December, 1990
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