Geometry of upper probabilities


Fabio Cuzzolin 
Proceedings of the International Symposium on Imprecise Probabilities and Their Applications (ISIPTA'03), 2003 

Abstract 
In this paper we adopt the geometric approach to the theory of evidence
to study the geometric counterparts of the plausibility functions, or upper
probabilities. The computation of the coordinate change between the two
natural reference frames in the belief space allows us to introduce the dual
notion of basic plausibility assignment and understand its relation with the
classical basic probability assignment. The convex shape of the plausibility
space P is recovered in analogy to what done for the belief space, and the
pointwise geometric relation between a belief function and the corresponding
plausibility vector is discussed. The orthogonal projection of an arbitrary
belief function s onto the probabilistic subspace is computed and compared
with other significant entities, such as the relative plausibility and mean probability
vectors. 
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Entry 
@inproceedings{cuzzolin03isipta,
AUTHOR = {F. Cuzzolin},
TITLE = {Geometry of Upper Probabilities},
JOURNAL = {ISIPTA'03},
VOLUME = {},
PAGES = {},
YEAR = {2003}
} 
