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Jeffreys' prior is the Hausdorff measure for the Hellinger and Kullback-Leibler distances

  • On a family F of probability measures on a measure space we consider the Hellinger and Kullback-Leibler distances. We show that under suitable regulari ty conditions Jeffreys' prior is proportional to the k-dimensional Hausdorff measure w.r.t. Hellinger dis tance respectively to the k2 -dimensional Hausdorff measure w.r.t. Kullback-Leibler distance. The proof i s based on an area-formula for the Hausdorff measure w.r.t. to generalized distances.

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Metadaten
Author:Werner Doster
URN (permanent link):urn:nbn:de:hbz:386-kluedo-7271
Document Type:Preprint
Language of publication:English
Year of Completion:1998
Year of Publication:1998
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011