Equivariant HPD credible sets and MAP estimators

Pierre Druilhet 1 Jean-Michel Marin 2, 3
2 SELECT - Model selection in statistical learning
Inria Saclay - Ile de France, LMO - Laboratoire de Mathématiques d'Orsay, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : 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.
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Bayesian Analysis, International Society for Bayesian Analysis, 2007, 2 (4), pp.681-692
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https://hal.inria.fr/inria-00077906
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Soumis le : mardi 6 juin 2006 - 09:59:04
Dernière modification le : jeudi 11 janvier 2018 - 06:22:14
Document(s) archivé(s) le : lundi 20 septembre 2010 - 14:07:19

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Pierre Druilhet, Jean-Michel Marin. Equivariant HPD credible sets and MAP estimators. Bayesian Analysis, International Society for Bayesian Analysis, 2007, 2 (4), pp.681-692. 〈inria-00077906v2〉

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