Belief-Function Formalism

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Belief-Function Formalism
Bayesian Formalism

• Computes the probability of a proposition

• Computes the probability that the evidence
  supports a proposition
• Also known as the Dempster-Shafer theory

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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).

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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.

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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

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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...

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Combining Belief Functions
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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.

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Uses

• Auditing
• Medical Diagnoses
• Or any other sort of application where
  information is gathered from semi-reliable
  sources.