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.
Publié le : 1990-12-14
Classification:
Noninformative priors,
Bayesian inference in group models,
maximal invariant,
62A05,
62F15,
62H20,
62H25
@article{1176347868,
author = {Chang, Ted and Eaves, David},
title = {Reference Priors for the Orbit in a Group Model},
journal = {Ann. Statist.},
volume = {18},
number = {1},
year = {1990},
pages = { 1595-1614},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347868}
}
Chang, Ted; Eaves, David. Reference Priors for the Orbit in a Group Model. Ann. Statist., Tome 18 (1990) no. 1, pp. 1595-1614. http://gdmltest.u-ga.fr/item/1176347868/