Open Access
February 1996 On the invariance of noninformative priors
Gauri Sankar Datta, Malay Ghosh
Ann. Statist. 24(1): 141-159 (February 1996). DOI: 10.1214/aos/1033066203


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.


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Gauri Sankar Datta. Malay Ghosh. "On the invariance of noninformative priors." Ann. Statist. 24 (1) 141 - 159, February 1996.


Published: February 1996
First available in Project Euclid: 26 September 2002

zbMATH: 0906.62024
MathSciNet: MR1389884
Digital Object Identifier: 10.1214/aos/1033066203

Primary: 62A05 , 62F15

Keywords: group invariance , group ordering , Jeffreys' prior , location-scale family , nuisance parameters , parameter of interest , parameter orthogonality , probability-matching equation , probability-matching priors , reference priors , reverse reference prior , spherically symmetric

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 1 • February 1996
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