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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

- 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.

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