Harmonizing discovery thresholds and reporting two-sided confidence intervals: a modified Feldman & Cousins method

TL;DR

This paper proposes a modification to the Feldman-Cousins method enabling the reporting of two-sided confidence intervals with a different, typically higher, significance level for excess detection, improving the flexibility of statistical reporting in physics searches.

Contribution

It introduces a modified Feldman-Cousins approach that allows for different confidence levels in reporting upper limits and discovery claims, addressing limitations of traditional methods.

Findings

Enables reporting of two-sided intervals with adjustable significance levels.

Maintains proper coverage properties despite modifications.

Provides a practical solution for physics experiments to communicate results more effectively.

Abstract

When searching for new physics effects, collaborations will often wish to publish upper limits and intervals with a lower confidence level than the threshold they would set to claim an excess or a discovery. However, confidence intervals are typically constructed to provide constant coverage, or probability to contain the true value, with possible overcoverage if the random parameter is discrete. In particular, that means that the confidence interval will contain the $0$-signal case with the same frequency as the confidence level. This paper details a modification to the Feldman-Cousins method to allow a different, higher excess reporting significance than the interval confidence level.