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