Combining upper limits with a Bayesian approach

TL;DR

This paper presents a Bayesian method for combining upper limits from independent measurements in low-count experiments, providing analytical insights and numerical tools for improved statistical inference.

Contribution

It introduces a Bayesian approach for combining upper limits in low-count experiments, supported by analytical formulas and a C++ program for practical implementation.

Findings

Analytical formulas for combining upper limits derived.

Numerical results demonstrate the method's effectiveness.

A C++ program (CULBA) is provided for practical use.

Abstract

We discuss how to determine and combine upper limits based on observed events and estimated backgrounds with a Bayesian method, when insignificant signals are observed in independent measurements. In addition to some general features deduced from the analytical formulae, systematic numerical results are obtained by a C$++$ program (CULBA) for low-count experiments, which can be used as a reference to combine two upper limits.