Treatment of the background error in the statistical analysis of Poisson processes

TL;DR

This paper presents a formalism for incorporating background error into the statistical analysis of Poisson processes, showing that neglecting background error can underestimate confidence intervals for the signal mean.

Contribution

It introduces a method to account for background error in Poisson process analysis, expanding confidence belts when background uncertainty is significant.

Findings

Background error significantly affects confidence intervals.

Neglecting background error underestimates uncertainty.

The formalism adjusts confidence belts accordingly.

Abstract

The formalism that allows to take into account the error sigma_b of the expected mean background b in the statistical analysis of a Poisson process with the frequentistic method is presented. It is shown that the error sigma_b cannot be neglected if it is not much smaller than sqrt(b). The resulting confidence belt is larger that the one for sigma_b=0, leading to larger confidence intervals for the mean mu of signal events.