Enhancing the physical significance of Frequentist confidence intervals

TL;DR

This paper compares Frequentist and Bayesian methods for confidence intervals, highlighting how their physical significance varies and proposing Bayesian Ordering as a preferable approach in certain cases.

Contribution

It introduces the Bayesian Ordering method, compares it with the Unified Approach, and discusses the physical significance of confidence intervals in statistical analysis.

Findings

Bayesian Ordering provides better physical significance.

Frequentist methods are statistically equivalent but differ in interpretation.

Critiques of both methods are addressed.

Abstract

It is shown that all the Frequentist methods are equivalent from a statistical point of view, but the physical significance of the confidence intervals depends on the method. The Bayesian Ordering method is presented and confronted with the Unified Approach in the case of a Poisson process with background. Some criticisms to both methods are answered. It is also argued that a general Frequentist method is not needed.