Properties of frequentist confidence levels derivatives

TL;DR

This paper investigates the derivatives of confidence levels used in high energy physics, providing a method to derive signal estimators, fit points, and integrate frequentist results into Bayesian analyses.

Contribution

It introduces a novel approach to interpret confidence levels as credible intervals, enabling better signal estimation and combination of results.

Findings

Derivatives of CL_s and CL_{s+b} can serve as signal estimators.

The method allows deriving best fit points and chi-squared functions.

Facilitates Bayesian combination of frequentist confidence level results.

Abstract

In high energy physics, results from searches for new particles or rare processes are often reported using a modified frequentist approach, known as $\rm{CL_s}$ method. In this paper, we study the properties of the derivatives of $\rm{CL_s}$ and $\rm{CL_{s+b}}$ as signal strength estimators if the confidence levels are interpreted as credible intervals. Our approach allows obtaining best fit points and $\chi^2$ functions which can be used for phenomenology studies. In addition, this approach can be used to incorporate $\rm{CL_s}$ results into Bayesian combinations.