Evaluation of two methods for incorporating a systematic uncertainty into a test of the background-only hypothesis for a Poisson process

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  • 19 February 2007
Abstract
Hypothesis tests for the presence of new sources of Poisson counts amidst background processes are frequently performed in high energy physics, gamma ray astronomy, and other branches of science. While there are conceptual issues already when the mean rate of background is precisely known, the issues are even more difficult when the mean background rate has non-negligible uncertainty, as some commonly used techniques are not on a sound foundation. In this paper, we evaluate two classes of algorithms by the criterion of how close the ensemble-average Type I error rate (rejection of the background-only hypothesis when it is true) compares with the nominal significance level given by the algorithm. Following J. Linnemann, we recommend wider use of an algorithm firmly grounded in frequentist tests of the ratio of Poisson means.

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