Fiducial Inference and Decision Theory

TL;DR

This paper explores the relationship between fiducial inference and decision theory, highlighting recent mathematical developments and clarifying their compatibility without requiring prior distributions.

Contribution

It explains and exemplifies how fiducial inference aligns with statistical decision theory, incorporating recent mathematical results to clarify their relationship.

Findings

Fiducial inference can be integrated with decision theory.

Recent mathematical results support the compatibility.

Fiducial approach offers an alternative to Bayesian methods.

Abstract

The majority of the statisticians concluded many decades ago that fiducial inference was nonsensical to them. Hannig et al. (2016) and others have, however, contributed to a renewed interest and focus. Fiducial inference is similar to Bayesian analysis, but without requiring a prior. The prior information is replaced by assuming a particular data generating equation. Berger (1985) explains that Bayesian analysis and statistical decision theory are in harmony. Taraldsen and Lindqvist (2013) show that fiducial theory and statistical decision theory also play well together. The purpose of this text is to explain and exemplify this together with recent mathematical results.