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Nonlinear Bayesian Estimation with Convex Sets of Probability Densities

Noack, Benjamin; Klumpp, Vesa; Brunn, Dietrich; Hanebeck, Uwe D.

Abstract:
This paper presents a theoretical framework for Bayesian estimation in the case of imprecisely known probability density functions. The lack of knowledge about the true density functions is represented by sets of densities. A formal Bayesian estimator for these sets is introduced, which is intractable for infinite sets. To obtain a tractable filter, properties of convex sets in form of convex polytopes of densities are investigated. It is shown that pathwise connected sets and their convex hulls describe the same ignorance. Thus, an exact algorithm is derived, which only needs to process the hull, delivering tractable results in the case of a proper parametrization. Since the estimator delivers a convex hull of densities as output, the theoretical grounds are laid for deriving efficient Bayesian estimators for sets of densities. The derived filter is illustrated by means of an example.


Zugehörige Institution(en) am KIT Institut für Anthropomatik (IFA)
Publikationstyp Proceedingsbeitrag
Jahr 2008
Sprache Englisch
Identifikator ISBN: 978-3-8007-3092-6
URN: urn:nbn:de:swb:90-348627
KITopen ID: 1000034862
Erschienen in Proceedings of the 11th International Conference on Information Fusion (Fusion 2008), June 30 2008-July 3, 2008
Verlag IEEE, Piscataway
Seiten 1-8
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