Fiducial inference: Difference between revisions

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</ref> and, also writing to Barnard, Fisher complained that his theory seemed to have only "an asymptotic approach to intelligibility".<ref name=Z/> Later Fisher confessed that "I don't understand yet what fiducial probability does. We shall have to live with it a long time before we know what it's doing for us. But it should not be ignored just because we don't yet have a clear interpretation".<ref name=Z/>
Lindley{{Citation needed|date=August 2011}}<ref>Sharon Bertsch McGrayne (2011) The Theory That Would Not Die. p. 133 {{full|date=November 2012}}</ref> showed that fiducial probability lacked additivity, and so was not a [[probability measure]]. Cox points out<ref>Cox (2006) p.66</ref> that the same argument applies to the so-called "[[Confidence Distribution|confidence distribution]]" associated with [[confidence intervals]], so the conclusion to be drawn from this is moot. Fisher sketched "proofs" of results using fiducial probability. When the conclusions of Fisher's fiducial arguments are not false, many have been shown to also follow from Bayesian inference.{{Citation needed|date=February 2010}}<ref name=KS/>
In 1978, JG Pederson wrote that "the fiducial argument has had very limited success and is now essentially dead."<ref>{{Cite journal|doi=10.2307/1402811|first=JG| last=Pederson| title=Fiducial Inference |journal=International Statistical Review | volume= 46 | year= 1978 | pages= 147–170 | mr=0514060 | issue= 2|postscript=<!--None-->|jstor=1402811 }}</ref> Davison<ref>Davison, A.C. (2001) "''Biometrika'' Centenary: Theory and general methodology" ''[[Biometrika]]'' 2001 (page 12 in the republication edited by D. M. Titterton and [[David R. Cox]])</ref> wrote "A few subsequent attempts have been made to resurrect fiducialism, but it now seems largely of historical importance, particularly in view of its restricted range of applicability when set alongside models of current interest."
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