1 / 8

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.

lesa
Télécharger la présentation

Belief-Function Formalism

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related