On Bayesian Treatment of Systematic Uncertainties in Confidence Interval Calculation
Abstract
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 (aka Feldman & Cousins) 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 to 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.
Cite
@article{arxiv.physics/0408039,
title = {On Bayesian Treatment of Systematic Uncertainties in Confidence Interval Calculation},
author = {Fredrik Tegenfeldt and Jan Conrad},
journal= {arXiv preprint arXiv:physics/0408039},
year = {2009}
}
Comments
19 pages, 7 figures, version to match the one accepted by NIM