Invariant HPD credible sets and MAP estimators

Abstract

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 invari-ant frequentist ML estimators. We also propose several adaptations in the case of nuisance parameters. © 2007 International Society for Bayesian Analysis.