Moving the Dempster-Shafer theory forward

Glenn Shafer
Friday, October 20 2:00-3:00
Bedford Library Seminar Room Royal Holloway

Thirty years ago, in 1976, I published A Mathematical Theory of Evidence. Five years later, Jeff Barnett dubbed its theory of belief functions the Dempster-Shafer theory. By 1986, this theory had achieved textbook status in artificial intelligence, and it has continued to flourish. A Google search using the exact string "Dempster-Shafer" produces about 180,000 hits. But in some important respects, the theory has not been moving forward. We still hear questions that were asked in the 1980s: How do we tell if bodies of evidence are independent? What do we do if they are dependent? And we still encounter confusion and disagreement about how to interpret the theory.

I think three things are needed to move the theory forward.

1. A richer understanding of the uses of probability. Dempster-Shafer is best regarded as a way of using probability. Understanding of this point is blocked by superficial but well entrenched dogmas.

2. A richer understanding statistical modeling. Mathematical statisticians and research workers in many other communities have become accustomed to beginning an analysis by specifying probabilities that are supposed known except for certain parameters. Dempster-Shafer modeling uses a different formal starting point, which may often be equally or more legitimate as a representation of actual knowledge.

3. Good examples. The elementary introductions to Dempster-Shafer theory that one finds in so many different domains are inadequate guides for dealing with the complications that arise in real problems. We need in-depth examples of sensible Dempster-Shafer analyses of a variety of problems of real scientific and technological importance.