Dempster-Shafer Theory SIU CS 537 4/12/11 and 4/14/11 Chet Langin.

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Presentation transcript:

Dempster-Shafer Theory SIU CS 537 4/12/11 and 4/14/11 Chet Langin

Dempster, A. P. (1967). "Upper and Lower Probabilities Induced by a Multivalued Mapping.“ The Annals of Mathematical Statistics 38(2): Shafer, G. (1976). A Mathematical Theory of Evidence, Princeton University Press.

What is Dempster-Shafer? Dempster-Shafer (D-S or DS) Mathematical theory of evidence. Data fusion. Degree of belief. Generalization of Bayes theory. Sets. Mass, not probability. “Bel Function” – Belief function

The D-S Environment

D-S Environment, Cont.

D-S vs. Probability

Non-belief vs. Ignorance

D-S Mass

Combining Evidence

D-S Rule of Combination

Example Combination Bomber = = 0.90 Bomber or Fighter = 0.07 Non-belief = 0.03

Range of Belief

What Would Make Plausibility < 1?

Evidential Interval

Example Evidential Intervals [1, 1]Completely True [0, 0]Completely False [0, 1]Completely Ignorant [Bel, 1]Tends to support [0, Pls]Tends to refute [Bel, Pls]Tends to both support & refute

Bel vs. Bel()

Bel() Example

Combination of 2 Bel()

The Normalization of Belief

A New Table

Normalization

Normalization, Cont. OK!

New Evidential Interval Belief | Plausibility | Disbelief Belief | Plausibility