Confidence belts on bounded parameters

TL;DR

This paper critiques the Feldman-Cousins method for confidence intervals on bounded parameters, showing it can yield null results, and proposes a modified Bayesian approach to avoid this issue with proper coverage.

Contribution

It identifies limitations of the Feldman-Cousins method and introduces a modified Bayesian approach to ensure no null results and correct coverage.

Findings

Feldman-Cousins method can produce null results for bounded parameters.

A modified Bayesian approach guarantees no null results.

The modified approach maintains proper statistical coverage.

Abstract

We show that the unified method recently proposed by Feldman and Cousins to put confidence intervals on bounded parameters cannot avoid the possibility of getting null results. A modified bayesian approach is also proposed (although not advocated) which ensures no null results and proper coverage.