Fiducial inference: Difference between revisions

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==Background==
 
The general approach of fiducial inference was proposed by [[Ronald Fisher]].<ref>{{cite journal | last1 = Fisher | first1 = R. A. | year = 1935 | title = The fiducial argument in statistical inference | journal = Annals of Eugenics | volume = 5 | issue = 4| pages = 391–398 | doi=10.1111/j.1469-1809.1935.tb02120.x| hdl = 2440/15222 | hdl-access = free }}</ref><ref>[http://www.hss.cmu.edu/philosophy/seidenfeld/relating%20to%20Fisher/Fisher's%20Fiducial%20Argument%20and%20Bayes%20Theorem.pdf R. A. Fisher's Fiducial Argument and Bayes' Theorem by Teddy Seidenfeld]</ref> Here "fiducial" comes from the Latin for faith. Fiducial inference can be interpreted as an attempt to perform [[inverse probability]] without calling on [[prior probability distribution]]s.<ref>Quenouille (1958), Chapter 6</ref> Fiducial inference quickly attracted controversy and was never widely accepted.<ref>Neyman, Jerzy. "Note on an article by Sir Ronald Fisher." Journal of the Royal Statistical Society. Series B (Methodological) (1956): 288–294.</ref> Indeed, counter-examples to the claims of Fisher for fiducial inference were soon published.{{Citation needed|date=June 2011}} These counter-examples cast doubt on the coherence of "fiducial inference" as a system of [[statistical inference]] or [[inductive logic]]. Other studies showed that, where the steps of fiducial inference are said to lead to "fiducial probabilities" (or "fiducial distributions"), these probabilities lack the property of additivity, and so cannot constitute a [[probability measure]].{{Citation needed|date=June 2011}}
 
The concept of fiducial inference can be outlined by comparing its treatment of the problem of [[interval estimation]] in relation to other modes of statistical inference.
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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/>
*Young, G. A., Smith, R. L. (2005) ''Essentials of Statistical Inference'', CUP. {{ISBN|0-521-83971-8}}
* {{cite journal | last1 = Fraser | first1 = D. A. S. | year = 1961 | title = The fiducial method and invariance | url = | journal = Biometrika | volume = 48 | issue = 3/4| pages = 261–80 | doi=10.2307/2332749| jstor = 2332749 }}
* {{cite journal | last1 = Fraser | first1 = D. A. S. | year = 1961 | title = On fiducial inference | url = | journal = Annals of Mathematical Statistics | volume = 32 | issue = 3| pages = 661–676 | doi=10.1214/aoms/1177704962| doi-access = free }}
 
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