The Annals of Statistics
- Ann. Statist.
- Volume 24, Number 1 (1996), 141-159.
On the invariance of noninformative priors
Jeffreys' prior, one of the widely used noninformative priors, remains invariant under reparameterization, but does not perform satisfactorily in the presence of nuisance parameters. To overcome this deficiency, recently various noninformative priors have been proposed in the literature.
This article explores the invariance (or lack thereof) of some of these noninformative priors including the reference prior of Berger and Bernardo, the reverse reference prior of J. K. Ghosh and the probability-matching prior of Peers and Stein under reparameterization. Berger and Bernardo's m-group ordered reference prior is shown to remain invariant under a special type of reparameterization. The reverse reference prior of J. K. Ghosh is shown not to remain invariant under reparameterization. However, the probability-matching prior is shown to remain invariant under any reparameterization. Also for spherically symmetric distributions, certain noninformative priors are derived using the principle of group invariance.
Ann. Statist. Volume 24, Number 1 (1996), 141-159.
First available in Project Euclid: 26 September 2002
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Jeffreys' prior reference priors group ordering reverse reference prior probability-matching equation probability-matching priors parameter orthogonality parameter of interest nuisance parameters location-scale family spherically symmetric group invariance
Datta, Gauri Sankar; Ghosh, Malay. On the invariance of noninformative priors. Ann. Statist. 24 (1996), no. 1, 141--159. doi:10.1214/aos/1033066203. http://projecteuclid.org/euclid.aos/1033066203.