Demystifying Inferential Models: A Fiducial Perspective

TL;DR

This paper explores the connections between inferential models, fiducial inference, and confidence curves, revealing that inferential models can be viewed as fiducial distribution-based confidence curves for uncertainty quantification.

Contribution

It provides a new perspective by linking inferential models to fiducial inference and introduces the concept of principle sets and assertions for probabilistic uncertainty quantification.

Findings

Inferential models can be interpreted as fiducial distribution-based confidence curves.

All probabilistic uncertainty quantification in inferential models relies on principle sets and assertions.

The paper clarifies the theoretical relationship between inferential models and fiducial inference.

Abstract

Inferential models have recently gained in popularity for valid uncertainty quantification. In this paper, we investigate inferential models by exploring relationships between inferential models, fiducial inference, and confidence curves. In short, we argue that from a certain point of view, inferential models can be viewed as fiducial distribution based confidence curves. We show that all probabilistic uncertainty quantification of inferential models is based on a collection of sets we name principle sets and principle assertions.