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Factorization of Dempster-Shafer Belief Functions
Based
on Data
798
Abstract
One important obstacle in applying Dempster-Shafer Theory (DST) is its
relationship to frequencies. In particular, there exist serious
difficulties in finding factorizations of belief functions from data.
In probability theory factorizations are usually
related to notion of (conditional) independence and their possibility
tested
accordingly. However, in DST conditional belief distributions prove to be
non-proper belief functions (that is ones connected with negative
"frequencies"). This makes statistical testing of potential conditional
independencies practically impossible, as no coherent interpretation
could be
found so far for negative belief function values.
In this paper a novel attempt is made to overcome this difficulty.
In the proposal no
conditional beliefs are calculated, but instead a new measure F is
introduced
within the framework of DST, closely related to conditional independence,
allowing to apply conventional statistical tests for detection of
dependence/independence.
Key words:Dempster Shafer Theory, negative conditional beliefs,
conditionally independent beliefs
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