Advertisement

Ploxoma: Testbed for Uncertain Inference

Part of the Lecture Notes in Statistics book series (LNS, volume 112)

Abstract

This paper compares two formalisms for uncertain inference, Kyburg’s Combinatorial Semantics and Dempster-Shafer belief function theory, on the basis of an example from the domain of medical diagnosis. I review Shafer’s example about the imaginary disease ploxoma and show how it would be represented in Combinatorial Semantics. I conclude that belief function theory has a qualitative advantage because it offers greater flexibility of expression, and provides results about more specific classes of patients. Nevertheless, a quantitative comparison reveals that the inferences sanctioned by Combinatorial Semantics are more reliable than those of belief function theory.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BlauKyburg94]
    H. Blau and H. E. Kyburg, Jr., “Ploxoma: Testbed for Uncertain Inference,” Technical Report 537, Department of Computer Science, University of Rochester, December 1994.Google Scholar
  2. [Dempster67]
    A. P. Dempster, “Upper and Lower Probabilities Induced by a Multivalued Mapping,” Annals of Mathematical Statistics, 38 (2): 325–339, April 1967.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [DempsterKong87]
    A. P. Dempster and A. Kong, “Commentary on Papers by Shafer, Lindley, and Spiegelhalter,” Statistical Science, 2 (1): 32–36, 1987.CrossRefGoogle Scholar
  4. [Diaconis78]
    P. Diaconis, “Review of ”A Mathematical Theory of Evidence“,” Journal of the American Statistical Association, 73 (363): 677–678, September 1978.CrossRefGoogle Scholar
  5. [DiaconisZabe1186]
    P. Diaconis and S. Zabell, “Some Alternatives to Bayes’s Rule,” In B. Grofman and G. Owen, editors, Information Pooling and Group Decision Making: Proceedings of the Second University of California, Irvine, Conference on Political Economy, pages 25–38. JAI Press, 1986.Google Scholar
  6. [Hunter87]
    D. Hunter, “Dempster-Shafer vs. Probabilistic Logic,” In Proceedings Third AAAI Workshop on Uncertainty in Artificial Intelligence, pages 22–29, University of Washington, Seattle, July 1987.Google Scholar
  7. [Kyburg83]
    H. E. Kyburg, Jr., “The Reference Class,” Philosophy of Science, 50: 374–397, 1983.MathSciNetCrossRefGoogle Scholar
  8. [Kyburg87]
    H. E. Kyburg, Jr., “Bayesian and Non-Bayesian Evidential Updating,” Artificial Intelligence, 31: 271–293, March 1987.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [Kyburg95]
    H. E. Kyburg, Jr., “Combinatorial Semantics,” Technical Report 563, Department of Computer Science, University of Rochester, January 1995.Google Scholar
  10. [Lemmer86]
    J. F. Lemmer, “Confidence Factors, Empiricism and the Dempster-Shafer Theory of Evidence,” In L. N. Kanal and J. F. Lemmer, editors, Uncertainty in Artificial Intelligence, pages 117–125. North-Holland, 1986.Google Scholar
  11. [Loui90]
    R. P. Loui, “Evidential Reasoning Compared in a Network Usage Prediciton Testbed: Preliminary Report,” In R. D. Shachter, T. S. Levitt, L. N. Kanal, and J. F. Lemmer, editors, Uncertainty in Artificial Intelligence 4, pages 253–269. North-Holland, 1990.Google Scholar
  12. [Pearl90]
    J. Pearl, “Reasoning with Belief Functions: An Analysis of Compatibility,” International Journal of Approximate Reasoning, 4 (5/6): 363–389, September/November 1990.MathSciNetzbMATHCrossRefGoogle Scholar
  13. [Shafer82]
    G. Shafer, “Belief Functions and Parametric Models,” Journal of the Royal Statistical Society, Series B (Methodological), 44 (3): 322–352, 1982.MathSciNetzbMATHGoogle Scholar
  14. [Smets9l]
    P. Smets, “About Updating,” In B. D. D’Ambrosio, P. Smets, and P. P. Bonissone, editors, Proceedings of the 7th Conference on Uncertainty in Artificial Intelligence, pages 378–385. Morgan Kaufmann, 1991.Google Scholar
  15. [Smets94]
    P. Smets, “What is Dempster-Shafer’s Model?,” In R. R. Yager, J. Kacprzyk, and M. Fedrizzi, editors, Advances in the Dempster-Shafer Theory of Evidence, chapter 1, pages 5–34. John Wiley & Sons, 1994.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • H. Blau
    • 1
  1. 1.Department of Computer ScienceUniversity of RochesterRochesterUSA

Personalised recommendations