Journal Article

On the Invariance of Noninformative Priors

Datta, Gauri Sankar, Ghosh, Malay

1996

Overview

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.

• Publisher: Institute of Mathematical Statistics,The Institute of Mathematical Statistics
• Subject: 62A05 / 62F15 / Bayes Theory / Bayesian analysis / Determinants / Differential equations / Exact sciences and technology / Fisher information / Frequentism / group invariance / group ordering / Jacobians / Jeffreys' prior / location-scale family / Mathematical foundations / Mathematical independent variables / Mathematics / nuisance parameters / One to one transformations / parameter of interest / parameter orthogonality / Parameterization / Parametric inference / Probability and statistics / probability-matching equation / probability-matching priors / reference priors / reverse reference prior / Sciences and techniques of general use / spherically symmetric / Statistics / Tradeoffs