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 = "9931008",
YEAR = "August 2007"
} 
