Abstract

Fiducial inference, introduced by Fisher in 1930, was conceived as a solution to what he perceived as a major shortcoming of the Bayesian approach: the reliance on a prior distribution for model parameters, even in the absence of prior information. However, fiducial inference sparked controversy among Fisher's contemporaries when it became evident that, beyond simple applications with a single parameter, it often resulted in procedures that were not exact in the frequentist sense and lacked some of the properties Fisher claimed.

This talk will discuss the ongoing efforts by the author and his collaborators to modify Fisher's fiducial approach, resulting in what they call Generalized Fiducial Inference (GFI). The talk will provide a concise introduction to GFI and explore its applications to various contemporary statistical problems.