Two new Bayesian approximations of  belief functions based on
  convex geometry


Fabio Cuzzolin
IEEE Transactions on Systems, Man, and Cybernetics - part B, 2007
 Abstract

In this paper we analyze from a geometric point of view the meaningful relations which take place between a belief function and the set of probability functions, in the framework of the geometric approach to the theory of evidence. Starting from the case of binary domains, we identify and study the three major geometric entities that relate a generic belief function to the set of probabilities P: the dual line connecting belief and plausibility functions, the orthogonal complement of P, and the simplex of consistent probabilities. These are in turn associated with different probability measures which depend on the original belief function. We describe in particular geometry and properties of the orthogonal projection of a belief function onto P and the intersection probability, provide their interpretations in terms of degrees of belief, and discuss their behavior with respect to convex closure.
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 BibTeX Entry

@article{cuzzolin07smcb, 
  AUTHOR = "Fabio Cuzzolin", 
  TITLE = "Two new Bayesian approximations of belief functions based on convex geometry",
  JOURNAL = "IEEE Transactions on Systems, Man, and Cybernetics - part B", 
  VOLUME = "37",
  NUMBER = "4",
  PAGES = "993--1008",
  YEAR = "August 2007" 
}

Oxford Brookes University