The Proper Fiducial Argument

  • F. Hampel
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4123)

Abstract

The paper describes the proper interpretation of the fiducial argument, as given by Fisher in (only) his first papers on the subject. It argues that far from being a quaint, little, isolated idea, this was the first attempt to build a bridge between aleatory probabilities (the only ones used by Neyman) and epistemic probabilities (the only ones used by Bayesians), by implicitly introducing, as a new type, frequentist epistemic probabilities. Some (partly rather unknown) reactions by other statisticians are discussed, and some rudiments of a new, unifying general theory of statistics are given which uses upper and lower probabilities and puts fiducial probability into a larger framework. Then Fisher’s pertaining 1930 paper is being reread in the light of present understanding, followed by some short sections on the (legitimate) aposteriori interpretation of confidence intervals, and on fiducial probabilities as limits of lower probabilities.

Keywords

Fiducial argument fiducial probability R.A. Fisher foundations of statistics statistical inference aleatory probabilities epistemic probabilities structure of epistemic probabilities upper and lower probabilities frequentist statistics axiom of frequentist epistemic probability Bayesian statistics intersubjective statistics bets odds fair bets successful bets confidence interval aposteriori interpretation of confidence intervals Neyman-Pearson statistics Behrens-Fisher problem 
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  • F. Hampel

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