Fiducial inference: Difference between revisions

→‎Background: give a ref and hence rm cite needed re Fisher
(Clarified the penultimate paragraph in "Background".)
(→‎Background: give a ref and hence rm cite needed re Fisher)
The general approach of fiducial inference was proposed by [[Ronald Fisher|]].<ref>['s%20Fiducial%20Argument%20and%20Bayes%20Theorem.pdf R. A. Fisher]].{{Citation's needed|date=JuneFiducial Argument and Bayes' Theorem by Teddy Seidenfeld]</ref> 2011}} 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.{{Citation needed|date=June 2011}} 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.