Significance in Gamma Ray Astronomy with Systematic Errors

TL;DR

This paper examines how systematic errors affect the calculation of gamma-ray signal significance using the Li and Ma method, proposing criteria and alternatives for accurate analysis in gamma-ray astronomy.

Contribution

It introduces a criterion to determine the applicability of the Li and Ma method with systematic errors and discusses an alternative approach for large errors.

Findings

Systematic errors can significantly impact significance calculations.

A simple criterion helps decide when Li and Ma is valid.

An alternative method is proposed for large systematic errors.

Abstract

The influence of systematic errors on the calculation of the statistical significance of a $\gamma$-ray signal with the frequently invoked Li and Ma method is investigated. A simple criterion is derived to decide whether the Li and Ma method can be applied in the presence of systematic errors. An alternative method is discussed for cases where systematic errors are too large for the application of the original Li and Ma method. This alternative method reduces to the Li and Ma method when systematic errors are negligible. Finally, it is shown that the consideration of systematic errors will be important in many analyses of data from the planned Cherenkov Telescope Array.