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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

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

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