R. A. Fisher and the fiducial argument

Sandy L Zabell*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

78 Scopus citations

Abstract

The fiducial argument arose from Fisher’s desire to create an inferential alternative to inverse methods. Fisher discovered such an alternative in 1930, when he realized that pivotal quantities permit the derivation of probability statements concerning an unknown parameter independent of any assumption concerning its a priori distribution. The original fiducial argument was virtually indistinguishable from the confidence approach of Neyman, although Fisher thought its application should be restricted in ways reflecting his view of inductive reasoning, thereby blending an inferential and a behaviorist viewpoint. After Fisher attempted to extend the fiducial argument to the multiparameter setting, this conflict surfaced, and he then abandoned the unconditional sampling approach of his earlier papers for the conditional approach of his later work. Initially unable to justify his intuition about the passage from a probabihty assertion about a statistic (conditional on a parameter) to a probabihty assertion about a parameter (conditional on a statistic), Fisher thought in 1956 that he had finally discovered the way out of this enigma with his concept of recognizable subset. But the crucial argument for the relevance of this concept was founded on yet another intuition-one which, now clearly stated, was later demonstrated to be false by Buehler and Feddersen in 1963.

Original languageEnglish (US)
Pages (from-to)369-387
Number of pages19
JournalStatistical Science
Volume7
Issue number3
DOIs
StatePublished - Jan 1 1992

Keywords

  • Behrens-Fisher problem
  • Fiducial inference
  • Jerzy Neyman
  • Maurice Bartlett
  • R. A. Fisher
  • Recognizable subsets

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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