Fiducial inference: Difference between revisions

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Lindley{{Citation needed|date=August 2011}}<ref>Sharon Bertsch McGrayne (2011) The Theory That Would Not Die. p. 133 {{full citation needed|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, J. G. Pederson wrote that "the fiducial argument has had very limited success and is now essentially dead".<ref>{{Cite journal|doi=10.2307/1402811|first=J. G. |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 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."<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>
 
However, fiducial inference is still being studied and its principles appear valuable for some scientific applications.<ref>{{cite journal | last1 = Hannig | first1 = J | year = 2009 | title = Generalized fiducial inference for wavelet regression | url = | journal = [[Biometrika]] | volume = 96 | issue = 4| pages = 847–860 | doi=10.1093/biomet/asp050}}</ref><ref>{{cite journal | last1 = Hannig | first1 = J | year = 2009 | title = On generalized fiducial inference | url = | journal = Statistica Sinica | volume = 19 | issue = | pages = 491–544 }}</ref> In the mid-2010s, the [[psychometrics|psychometrician]] [[Yang Liu (psychometrician)|Yang Liu]] developed generalized fiducial inference for models in [[item response theory]] and demonstrated favorable results compared to frequentist and Bayesian approaches. Other current work in fiducial inference is ongoing under the name of [[confidence distribution]]s.
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