A Generalization of Bayesian Inference

  • Arthur P. Dempster
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 219)

Abstract

Procedures of statistical inference are described which generalize Bayesian inference in specific ways. Probability is used in such a way that in general only bounds may be placed on the probabilities of given events, and probability systems of this kind are suggested both for sample information and for prior information. These systems are then combined using a specified rule. Illustrations are given for inferences about trinomial probabilities, and for inferences about a monotone sequence of binomial pi. Finally, some comments are made on the general class of models which produce upper and lower probabilities, and on the specific models which underlie the suggested inference procedures.

Keywords

Lower Probability Bayesian Inference Prior Information Uncertainty Principle Product Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boole, G. (1854). An Investigation of the Laws of Thought. New York: Reprinted by Dover (1958).Google Scholar
  2. Dempster, A. P. (1966). New methods for reasoning towards posterior distributions based on sample data. Ann. Math. Statist., 37, 355–74.CrossRefMathSciNetGoogle Scholar
  3. Dempster, A. P. (1967a). Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Statist., 38, 325–39.Google Scholar
  4. Dempster, A. P. (1967b). Upper and lower probability inferences based on a sample from a finite univariate population. Biometrika, 54, 515–528.Google Scholar
  5. Good, I. J. (1962). The measure of a non-measurable set. Logic, Methodology and Philosophy of Science (edited by Ernest Nagel, Patrick Suppes and Alfred Tarski), pp. 319–329. Stanford University Press.Google Scholar
  6. Lindley, D. V. (1958). Fiducial distributions and Bayes’ theorem. J. R. Statist. Soc. B, 20, 102–107.MATHMathSciNetGoogle Scholar
  7. Smith, C. A. B. (1961). Consistency in statistical inference and decision (with discussion). J. R. Statist. Soc. B, 23, 1–25.MATHGoogle Scholar
  8. Smith, C. A. B. (1965). Personal probability and statistical analysis (with discussion). J. R. Statist. Soc. A, 128, 469–499.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Arthur P. Dempster

There are no affiliations available

Personalised recommendations