Bayesian Analysis

Invariant {HPD} credible sets and {MAP} estimators

Pierre Druilhet and Jean-Michel Marin

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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.

Article information

Bayesian Anal., Volume 2, Number 4 (2007), 681-691.

First available in Project Euclid: 22 June 2012

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Bayesian statistics HPD MAP Jeffreys measure nuisance parameters reference prior


Druilhet, Pierre; Marin, Jean-Michel. Invariant {HPD} credible sets and {MAP} estimators. Bayesian Anal. 2 (2007), no. 4, 681--691. doi:10.1214/07-BA227.

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