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New Methods for Reasoning Towards Posterior Distributions Based on Sample Data

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

Abstract

This paper redefines the concept of sampling from a population with a given parametric form, and thus leads up to some proposed alternatives to the existing Bayesian and fiducial arguments for deriving posterior distributions. Section 2 spells out the basic assumptions of the suggested class of sampling models, and Sect. 3 suggests a mode of inference appropriate to the sampling models adopted. A novel property of these inferences is that they generally assign upper and lower probabilities to events concerning unknowns rather than precise probabilities as given by Bayesian or fiducial arguments. Sections 4 and 5 present details of the new arguments for binomial sampling with a continuous parameter p and for general multinomial sampling with a finite number of contemplated hypotheses. Among the concluding remarks, it is pointed out that the methods of Sect. 5 include as limiting cases situations with discrete or continuous observables and continuously ranging parameters.

Keywords

Posterior Distribution Prior Distribution Sampling Model Population Individual Probability Judgment 
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.

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References

  1. Dempster, A. P. (1963). On direct probabilities. J.Roy. Statist. Soc. Ser. B bf 20 102–107.MathSciNetGoogle Scholar
  2. Dempster, A. P. (1964). On the difficulties inherent inFisher’s fiducial argument. J. Amer. Statist. Assoc. bf59 56–66.CrossRefMathSciNetGoogle Scholar
  3. Dempster , A. P. (1965). On a class of mathematical structures yielding upper and lower probabilities. npublished research report.Google Scholar
  4. Todhunter , I. (1865). A History of the Mathematical Theory of Probability. Reprinted (1949) by Chelsea, New York.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Arthur P. Dempster

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