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Dissonance and Consistency according to Shackle and Shafer

Published online by Cambridge University Press:  31 January 2023

Isaac Levi
Isaac Levi*
Affiliation:
Columbia University
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R.A.Fisher introduced the fiducial argument as a means for obtaining something from nothing. He thought that on some occasions it was legitimate to obtain a posterior probability distribution over a range of simple statistical hypotheses without commitment to a prior distribution [4].

H.Jeffreys thought he could tame Fisher by casting his argument in a Bayesian mold through a derivation of the fiducial posterior from a suitably constructed ignorance prior via Bayes’ theorem and conditionalization on the data of experimentation. According to Jeffreys, Fisher was using something to obtain something after all ([7],pp.381-383).

D.V.Lindley furthered the process of taming by specifying allegedly necessary and sufficient conditions for the consistency of fiducial reasoning in contexts of one parameter estimation with Bayesian requirements [14]. I. Hacking exploited Lindley’s result to supply his own ingenious method for taming Fisher([5],ch. 9).

T.Seidenfeld has recently demonstrated that Lindley’s conditions are insufficient for consistency and that reconstructions like Jeffreys’ or Hacking’s lead to contradiction ([15], PP. 721-727).

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. 466 - 477
Copyright
Copyright © 1981 Philosophy of Science Association

References

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