Status of The Approach
After its formulation by Fisher, fiducial inference quickly attracted controversy and was never widely accepted. Indeed, counter-examples to the claims of Fisher for fiducial inference were soon published.
Fisher admitted that "fiducial inference" had problems. Fisher wrote to George A. Barnard that he was "not clear in the head" about one problem on fiducial inference, and, also writing to Barnard, Fisher complained that his theory seemed to have only "an asymptotic approach to intelligibility". 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".
Lindley showed that fiducial probability lacked additivity, and so was not a probability measure. Cox points out that the same argument applies to the so-called "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.
In 1978, JG Pederson wrote that "the fiducial argument has had very limited success and is now essentially dead." 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."
However, fiducial inference is still being studied and other current work is ongoing under the name of confidence distributions.
Read more about this topic: Fiducial Inference
Famous quotes containing the words status of, status and/or approach:
“What is clear is that Christianity directed increased attention to childhood. For the first time in history it seemed important to decide what the moral status of children was. In the midst of this sometimes excessive concern, a new sympathy for children was promoted. Sometimes this meant criticizing adults. . . . So far as parents were put on the defensive in this way, the beginning of the Christian era marks a revolution in the child’s status.”
—C. John Sommerville (20th century)
“At all events, as she, Ulster, cannot have the status quo, nothing remains for her but complete union or the most extreme form of Home Rule; that is, separation from both England and Ireland.”
—George Bernard Shaw (1856–1950)
“I am always glad to think that my education was, for the most part, informal, and had not the slightest reference to a future business career. It left me free and untrammeled to approach my business problems without the limiting influence of specific training.”
—Alice Foote MacDougall (1867–1945)