, Volume 123, Issue 3, pp 347–364 | Cite as

Connecting Dempster–Shafer Belief Functions with Likelihood-based Inference

  • Mikel Aickin


The Dempster–Shafer approach to expressing beliefabout a parameter in a statistical model is notconsistent with the likelihood principle. Thisinconsistency has been recognized for some time, andmanifests itself as a non-commutativity, in which theorder of operations (combining belief, combininglikelihood) makes a difference. It is proposed herethat requiring the expression of belief to be committed to the model (and to certain of itssubmodels) makes likelihood inference very nearly aspecial case of the Dempster–Shafer theory.


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  1. Birnbaum, A.: 1962, 'On the Foundations of Statistical Inference' (with discussion), Journal of the American Statistical Association 57, 269–326.Google Scholar
  2. Clayton, D. and M. Hills: 1993, Statistical Models in Epidemiology, Oxford University Press, Oxford, UK.Google Scholar
  3. Edwards, A. W. F.: 1972, Likelihood, Cambridge University Press, Cambridge, UK.Google Scholar
  4. Royall, R. M.: 1997, Statistical Evidence: A Likelihood Paradigm, Chapman and Hall, London, UK.Google Scholar
  5. Shafer, G.: 1976, A Mathematical Theory of Evidence, Princeton University Press, Princeton, NJ.Google Scholar
  6. Shafer, G.: 1982, 'Belief Functions and Parametric Models' (with discussion), Journal of the Royal Statistical Society, Series B 44, 322–52.Google Scholar
  7. Yager, R. R., J. Kacprzyk, M. Fedrizzi (eds.): 1994, Advances in the Dempster-Shafer Theory of Evidence, John Wiley & Sons, New York, NY.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Mikel Aickin
    • 1
  1. 1.Center for Health ResearchPortlandU.S.A.

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