A revision to the theory of organic fiducial inference

TL;DR

This paper revises the principle underlying organic fiducial inference, enabling Bayesian methods to play a minor role and allowing more data information to influence the fiducial density in specific cases.

Contribution

It introduces a natural modification to the core principle of organic fiducial inference, enhancing its flexibility and integration with Bayesian ideas.

Findings

The revised principle allows for partial Bayesian influence.

Application to previous examples shows improved data incorporation.

The modification broadens the applicability of fiducial inference.

Abstract

A principle is modified that underlies the theory of organic fiducial inference as this theory was presented in an earlier paper. This modification, which is arguably a natural one to make, allows Bayesian inference to sometimes have a minor role within the theory in question and, as a consequence, allows more information from the data to be incorporated into the way a full conditional fiducial density is defined in certain cases. The new version of the principle concerned is applied to examples that were analysed previously using the older version of this principle.