Belief-Function Formalism

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# Belief-Function Formalism - PowerPoint PPT Presentation

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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Presentation Transcript

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
• 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...
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.