Fiducial inference introduced the pivotal inversion that is central to modern confidence theory. Initially this provided confidence bounds but later was generalized to give confidence distributions on the paramseter space. For this it came in direct conflict with the then prominent Bayesian approach called inverse probability. Confidence distributions are now however widespread in modern likelihood theory. Recent results from this theory indicate that the developed fiducial confidence approach is giving a consistent statement of where the parameter is with respect to the data, and indeed is consistent with recent Bayesian approaches that allow data dependent priors.
KeywordsBayesian inference Confidence theory Fiducial inference Frequentist school Inverse probability Likelihood Markov chain Monte Carlo methods
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