These are rules, intended for general application, by which conclusions can be drawn from samples of data.
Some current research in statistical methodology is either explicitly linked to fiducial inference or is closely connected to it.
Such problems related to the need to assign a prior distribution to the unknown values.
The aim was to have a procedure, like the Bayesian method, whose results could still be given an inverse probability interpretation based on the actual data observed.
[6] Fisher required the existence of a sufficient statistic for the fiducial method to apply.
The calculation is identical to the pivotal method for finding a confidence interval, but the interpretation is different.
[citation needed] Notice that the fiducial distribution is uniquely defined when a single sufficient statistic exists.
However, this is only equivalent to the fiducial method if the pivotal quantity is uniquely defined based on a sufficient statistic.
[citation needed] Fisher would have denied that this interpretation is correct: for him, the fiducial distribution had to be defined uniquely and it had to use all the information in the sample.
When the conclusions of Fisher's fiducial arguments are not false, many have been shown to also follow from Bayesian inference.
[citation needed][6] In 1978, J. G. Pederson wrote that "the fiducial argument has had very limited success and is now essentially dead".
[10] 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.