Invariant HPD credible sets and MAP estimators. (English) Zbl 1331.62136

Summary: 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.


62F15 Bayesian inference
65C60 Computational problems in statistics (MSC2010)
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