Another Look at Confidence Intervals: Proposal for a More Relevant and Transparent Approach

TL;DR

This paper critically examines confidence interval methods, especially in low-statistics scenarios, highlighting issues and proposing a more pragmatic, transparent approach to improve their relevance and interpretation.

Contribution

It introduces a practical, self-consistent framework for confidence intervals that addresses common misconceptions and enhances their interpretability in scientific research.

Findings

Confidence intervals are often misinterpreted and misapplied.

Current methods can lead to paradoxical behaviors in low-statistics regions.

A pragmatic approach improves transparency and relevance of confidence bounds.

Abstract

The behaviors of various confidence/credible interval constructions are explored, particularly in the region of low statistics where methods diverge most. We highlight a number of challenges, such as the treatment of nuisance parameters, and common misconceptions associated with such constructions. An informal survey of the literature suggests that confidence intervals are not always defined in relevant ways and are too often misinterpreted and/or misapplied. This can lead to seemingly paradoxical behaviours and flawed comparisons regarding the relevance of experimental results. We therefore conclude that there is a need for a more pragmatic strategy which recognizes that, while it is critical to objectively convey the information content of the data, there is also a strong desire to derive bounds on models and a natural instinct to interpret things this way. Accordingly, we attempt to put aside philosophical biases in favor of a practical view to propose a more transparent and self-consistent approach that better addresses these issues.