Physics – High Energy Physics – High Energy Physics - Experiment
Scientific paper
2002-06-14
Physics
High Energy Physics
High Energy Physics - Experiment
6 pages, 3 figures. To appear in: Proceedings of Conference on Advanced Statisical Techniques in Particle Physics, Durham, 200
Scientific paper
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.
Botner Olga
Conrad Jan
Hallgren Allan
los Heros Carlos Pérez de
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