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Lindley{{Citation neededdate=August 2011}}<ref>Sharon Bertsch McGrayne (2011) The Theory That Would Not Die. p. 133 {{full citation neededdate=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 socalled "[[Confidence Distributionconfidence 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 neededdate=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 journaldoi=10.2307/1402811first=J. G. last=Pederson title=Fiducial Inference journal=International Statistical Review volume= 46 year= 1978 pages= 147–170 mr=0514060 issue= 2
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 mid2010s, the [[psychometricspsychometrician]] [[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.
