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.

19 pages, 7 figures, version to match the one accepted by NIM

References in corpus (2)

• Limits and Confidence Intervals in the Presence of Nuisance Parameters
• Search for the Flavor-Changing Neutral Current Decay $D^0\to {\mu }^{+}{\mu }^{-}$ with the HERA-B Detector

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