Transcript Belief-Function Formalism

Bayesian Formalism
• Computes the probability of a proposition
Belief-Function Formalism
• Computes the probability that the evidence
supports a proposition
• Also known as the Dempster-Shafer theory
Bayesian Formalism
• There is an 90% chance that the department
is following a procedure and 10% chance
they are not.
Belief-Function Formalism
• We have a 90% reason to believe that the
department is following procedure but no
reason not to (0%).
Belief Function
• Written as Bel(x)
• Measures the likelihood that the evidence
supports x.
• Where x is a subset of of some set S that
represents the range of possible choices.
• For example let S be the set of possible
causes for a disease.
Basic Probability Assignment
(bpa)
• The impact of each distinct piece of
evidence on the subsets of S is represented
as a function known as the bpa.
• It is a generalization of the traditional
probability density function.
• For example…
The Belief Function
• The Bel(x) is then the sum of the bpas of all
the possible subsets of x which in tern is a
subset of S.
• The Bel(S) is always 1.
• The Bel(Ø), the empty set, is always 0.
• For example...
Combining Belief Functions
The Belief-Function
Formalization ...
• Provides a way to represent ignorance in
ways that the Bayesian formalism can not.
• Looks at questions of interest in a more
indirect way.
• Is in fact a generalization of the Bayesian
formalization.
Uses
• Auditing
• Medical Diagnoses
• Or any other sort of application where
information is gathered from semi-reliable
sources.