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On Bayesian Treatment of Systematic Uncertainties in Confidence Interval Calculation | | Fredrik Tegenfeldt
; Jan Conrad
; | | Date: |
8 Aug 2004 | | Journal: | Nucl.Instrum.Meth. A539 (2005) 407-413 | | Subject: | Data Analysis, Statistics and Probability | physics.data-an astro-ph hep-ex | | Affiliation: | ISU & CERN), Jan Conrad (CERN | | 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. | | Source: | arXiv, physics/0408039 | | Services: | Forum | Review | PDF | Favorites | |
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