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Bayesian Formalism. Belief-Function Formalism. Computes the probability of a proposition. Computes the probability that the evidence supports a proposition Also known as the Dempster-Shafer theory. Bayesian Formalism.

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Belief-Function Formalism

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Belief function formalism l.jpg

Bayesian Formalism

Belief-Function 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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  • Auditing

  • Medical Diagnoses

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

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