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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.

MSC:

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