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December 2007 Invariant {HPD} credible sets and {MAP} estimators
Pierre Druilhet, Jean-Michel Marin
Bayesian Anal. 2(4): 681-691 (December 2007). DOI: 10.1214/07-BA227


MAP estimators and HPD credible sets are often criticized in the literature because of paradoxical behaviour due to a lack of invariance 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 invariant frequentist ML estimators. We also propose several adaptations in the case of nuisance parameters.


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Pierre Druilhet. Jean-Michel Marin. "Invariant {HPD} credible sets and {MAP} estimators." Bayesian Anal. 2 (4) 681 - 691, December 2007.


Published: December 2007
First available in Project Euclid: 22 June 2012

zbMATH: 1331.62136
MathSciNet: MR2361970
Digital Object Identifier: 10.1214/07-BA227

Keywords: Bayesian statistics , HPD , Jeffreys measure , MAP , nuisance parameters , reference prior

Rights: Copyright © 2007 International Society for Bayesian Analysis


Vol.2 • No. 4 • December 2007
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