Including Systematic Uncertainties in Confidence Interval Construction for Poisson Statistics

TL;DR

This paper develops a method to incorporate systematic uncertainties into confidence interval calculations for Poisson statistics, accounting for various uncertainties and correlations, and evaluates its coverage properties.

Contribution

It introduces an improved method that integrates systematic uncertainties into confidence interval construction, applicable to background and efficiency uncertainties with correlations, using Feldman & Cousins approach.

Findings

Method accounts for multiple systematic uncertainties.

Coverage tests demonstrate the method's reliability.

Application to dark matter searches illustrates impact of uncertainties.

Abstract

One way to incorporate systematic uncertainties into the calculation of confidence intervals is by integrating over probability density functions parametrizing the uncertainties. In this note we present a development of this method which takes into account uncertainties in the prediction of background processes, uncertainties in the signal detection efficiency and background efficiency and allows for a correlation between the signal and background detection efficiencies. We implement this method with the Feldman & Cousins unified approach with and without conditioning. We present studies of coverage for the Feldman & Cousins and Neyman ordering schemes. In particular, we present two different types of coverage tests for the case where systematic uncertainties are included. To illustrate the method we show the relative effect of including systematic uncertainties the case of dark matter search as performed by modern neutrino tel escopes.