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Belief-Function Formalism

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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  1. 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

  2. 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%).

  3. 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.

  4. 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…

  5. 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...

  6. Combining Belief Functions

  7. 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.

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

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