Equivariant HPD credible sets and MAP estimators

Druilhet, Pierre; Marin, Jean-Michel

Druilhet, Pierre; Marin, Jean-Michel (2007), Equivariant HPD credible sets and MAP estimators, Bayesian Analysis, 2, 4, p. 681-692. http://dx.doi.org/10.1214/07-BA227

Type

Article accepté pour publication ou publié

External document link

http://hal.inria.fr/inria-00077906/en/

Date

2007

Journal name

Bayesian Analysis

Volume

Number

Publisher

International Society for Bayesian Analysis

ISBN

ISSN 0249-6399

Pages

681-692

Abstract (EN)

MAP estimators and HPD credible sets are often criticized in the literature because of paradoxical behaviour due to a lack of equivariance under reparametrization. In this paper, we propose a new version of MAP estimators and HPD credible sets that avoid this undesirable feature. Moreover, in the special case of non-informative prior, the new MAP estimators coincide with the equivariant frequentist ML estimators. We also propose several adaptations in the case of nuisance parameters.

Subjects / Keywords

Bayesian statistics; Reference prior; Nuisance parameters; Jeffreys measure; HPD; MAP