Fiducial inference then and now

TL;DR

This paper reviews the history, development, and resurgence of fiducial inference, emphasizing the functional model formulation to clarify its applicability and limitations in statistical inference.

Contribution

It provides a comprehensive historical overview and clarifies the conditions under which fiducial inference can be applied unambiguously using the functional model approach.

Findings

Fiducial inference has a limited but well-defined domain of applicability.

The functional model formulation clarifies when fiducial inference is valid.

Recent resurgence highlights renewed interest in fiducial methods.

Abstract

We conduct a review of the fiducial approach to statistical inference, following its journey from its initiation by R. A. Fisher, through various problems and criticisms, on to its general neglect, and then to its more recent resurgence. Emphasis is laid on the functional model formulation, which helps clarify the very limited conditions under which fiducial inference can be conducted in an unambiguous and self-consistent way.