Fiducial on a string

TL;DR

This paper analyzes a fiducial inference example involving a parameter restricted to a string, highlighting ongoing interest and challenges in fiducial and Bayesian methods for constrained parameters.

Contribution

It provides a detailed analysis of a fiducial distribution constrained to a string, illustrating complexities in inference with restricted parameter spaces.

Findings

Fiducial distribution can be restricted to a string in parameter space.

The example highlights challenges in uncertainty quantification for constrained parameters.

The analysis connects fiducial inference with Bayesian and manifold-based approaches.

Abstract

The fiducial argument of Fisher (1973) has been described as his biggest blunder, but the recent review of Hannig et al. (2016) demonstrates the current and increasing interest in this brilliant idea. This short note analyses an example introduced by Seidenfeld (1992) where the fiducial distribution is restricted to a string. Keywords and phrases: Bayesian and fiducial inference, Restrictions on parameters, Uncertainty quantification, Epistemic probability, Statistics on a manifold.