The proper fiducial argument
Frank Hampel
February 2003
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.
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