B0435
Title: Confidence in Bayesian and fiducial inference
Authors: Gunnar Taraldsen - NTNU Norway (Norway) [presenting]
Abstract: Fiducial inference has not been widely accepted. Different versions are presented in textbooks and most often with critical remarks. Fiducial inference was, in fact, declared dead at the end of the last century. There is little confidence in fiducial inference. In contrast, others suggested that maybe Fisher's biggest blunder will become a big hit in the 21st century. One reason for this optimism is the version of fiducial inference based on a data-generating model. This is perfectly adapted to the available computational power in the 21st century. We have much confidence in fiducial inference. We present results that ensure that a fiducial distribution is a confidence distribution. Similarly, conditions are given that ensure that a fiducial is a Bayes posterior. Our main example is the correlation in a binormal distribution as used initially in 1930 when Fisher introduced the fiducial argument. An exact formula for the confidence density of the correlation has recently been derived, and this allows illustrating the theory more directly than before.
