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  A Mathematical Theory of Evidence

Glenn Shafer
Princeton University Press, 1976.


This book was published by the Princeton University Press in 1976.

The author was an assistant professor at Princeton University when the book was written. The first paragraph of his preface reads as follows:

    In the spring of 1971, I attended a course on statistical inference taught by Arthur Dempster at Harvard. In the fall of that same year Geoffrey Watson suggested I give a talk expositing Dempster's work on upper and lower probabilities to the Department of Statistics at Princeton. This essay is one of the results of the ensuing effort. It offers a reinterpretation of Dempster's work, a reinterpretation that identifies his "lower probabilities" as epistemic probabilities or degrees of belief, takes the rule for combining such degrees of belief as fundamental, and abandons the idea that they arise as lower bounds over classes of Bayesian probabilities.

Jeff Barnet, one of the computer scientists who introduced the book's theory to the artificial intelligence community in the late 1970s and early 1980s, called the theory "the Dempster-Shafer theory," and this name has stuck.

Recent Work on the Dempster-Shafer Theory

A search on the web will reveal thousands of discussions, applications, and extensions of the Dempster-Shafer theory. Here are a few references that may be particularly useful.

  1. Constructive Decision Theory, by Glenn Shafer.  Department of Mathematics, University of Kansas.  December, 1982.  The appendix of this paper evolved into Savage revisited (with discussion). Statistical Science 1 463-501. 1986.  But the body of the paper, which includes a discussion of using belief functions in decision making based on goals, was never published.  A similar concept of goal-based decision making is discussed by David Krantz and Howard Kunreuther in “Goals and plans in decision making,” Judgement and Decision Making 2(3):137-168, 2007.
  2. Advances in the Dempster-Shafer Theory of Evidence, edited by Ronald R. Yager, Mario Fedrizzi, and Janusz Kacprzyk. Wiley. 1994.

  3. Special Issue on Dempster-Shafer Theory, Methodology, and Applications. International Journal of Approximate Reasoning. Volume 31, Numbers 1-2, October 2002.

  4. Belief Functions in Business Decision: Studies in Fuzziness and Soft Computing, Srivastava, R. J. and Mock, T.J.; Physica-Verlag Heidelberg: New York, 2002.

  5. Classic Works of the Dempster-Shafer Theory of Belief Functions, edited by Ronald Yager and Liping Liu, February, 2008, Springer.  ISBN: 978-3-540-25381-5.

  6. The Dempster–Shafer calculus for statisticians, by A. P. Dempster, International Journal of Approximate Reasoning, 2008.


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