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

2. Belief-Function Formalism We have a 90% reason to believe that the department is following procedure but no reason not to (0%). Bayesian Formalism There is an 90% chance that the department is following a procedure and 10% chance they are not.

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.