On Bayesian treatment of systematic uncertainties in confidence interval calculation

In high energy physics, a widely used method to treat systematic uncertainties in confidence interval calculations is based on combining a frequentist construction of confidence belts with a Bayesian treatment of systematic uncertainties. In this note we present a study of the coverage of this method for the standard Likelihood Ratio (Feldman and Cousins Phys. Rev. D 57 (1998) 3873) construction for a Poisson process with known background and Gaussian or log-Normal distributed uncertainties in the background or signal efficiency. For uncertainties in the signal efficiency of upto 40% we find over-coverage on the level of 2-4% depending on the size of uncertainties and the region in signal space. Uncertainties in the background generally have smaller effect on the coverage. A considerable smoothing of the coverage curves is observed. A software package is presented which allows fast calculation of the confidence intervals for a variety of assumptions on shape and size of systematic uncertainties for different nuisance parameters. The calculation speed allows experimenters to test the coverage for their specific conditions. (C) 2004 Elsevier B.V. All rights reserved.