Coverage Of Confidence Intervals For Poisson Statistics In Presence Of Systematic Uncertainties

J. Conrad, O. Botner, A. Hallgren, C. P. de los Heros

Published 2002-06-14Version 1

In this note we consider coverage of confidence intervals calculated with and without systematic uncertainties. These calculations follow the prescription originally proposed by Cousins & Highland but here extended to account for different shapes, size and types of systematic uncertainties. Also two different ordering schemes are considered: the Feldman & Cousins ordering and its variant where conditioning on the background expectation is applied as proposed by Roe & Woodroofe. Without uncertainties Feldman & Cousins method over-covers as expected because of the discreteness of the Poisson distribution. For Roe & Woodroofe's method we find under-coverage for low signal expectations. When including uncertainties it becomes important to define the ensemble for which the coverage is determined. We consider two different ensembles, where in ensemble A all nuisance parameters are fixed and in ensemble B the nuisance parameters are varied according to their uncertainties. We also discuss the subtleties of the realization of the ensemble with varying systematic uncertainties.