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Statistical Evidence and Belief Functions

Published online by Cambridge University Press:  31 January 2023

Teddy Seidenfeld
Teddy Seidenfeld*
Affiliation:
University of Pittsburgh
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In his recent monograph [7], Professor Shafer has offered us an alternative to Bayesian inference with his novel theory of belief functions and, in his current paper [8], has characterized his position by pointing to two basic differences it shares with Bayesianism. First, belief functions are non-additive so that the degree of belief assigned to the disjunction ‘A1 or A2’ may be larger than the sum of the degrees of belief assigned to the separate disjuncts. Second, the theory of belief functions has its own rule for determining the commitments to changes in degrees of belief when evidence is compounded. So, instead of the Bayesian postulate of conditionalization, that is, in place of using Bayes’ theorem to identify the commitments to changes in probability when evidence accumulates, the theory advocated by Professor Shafer relies on a proposal he traces to A.P.Dempster, which he calls Dempster’s rule for combination of belief functions.

Type
Part XI. Statistical Evidence
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1978 , Issue 2: Volume Two: Symposia and Invited Papers 1978 , 1978 , pp. 478 - 489
Copyright
Copyright © 1981 Philosophy of Science Association

References

[1] Barnard, G. and Sprott, D.A. “A Note on Basu’s Examples of Anomalous Ancillary Statistics.” In Foundations of Statistical Inference. Edited by Godambe, V.P. Montreal: Holt, Rinehart and Winston, 1970. Pages 163–170.Google Scholar
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[5] Levi, I. “Dissonance and Consistency According to Shackle and Shafer.” In PSA 1978, Volume 2. Edited by Asquith, P.D. and Hacking, I. East Lansing, Michigan: Philosophy of Science Association, 1981. Pages 466–477.Google Scholar
[6] Savage, L. “Subjective Probability and Statistical Practice.” In The Foundations of Statistical Inference. Edited by Savage, L. et al. London: Methuen, 1962. Pages 9–35.Google Scholar
[7] Shafer, G. A Mathematical Theory of Evidence. Princeton: Princeton University Press, 1976.CrossRefGoogle Scholar
[8] Shafer, G. “Two Theories of Probability.” In PSA 1978, Volume 2. Edited by Asquith, P.D. and Hacking, I. East Lansing, Michigan. Philosophy of Science Association, 1981. Pages 441–465.Google Scholar