paper

Frequentist Coverage Properties of Uncertainty Intervals for Weak Poisson Signals in the Presence of Background

arXiv:0804.4032 · doi:10.1088/0957-0233/21/3/035102

Abstract

We construct uncertainty intervals for weak Poisson signals in the presence of background. We consider the case where a primary experiment yields a realization of the signal plus background, and a second experiment yields a realization of the background. The data acquisitions times for the background-only experiment,T_bg, and the primary experiment,T, are selected so that their ratio varies from 1 to 25. The expected number of background counts in the primary experiment varies from 0.2 to 2. We construct 90 and 95 percent confidence intervals based on a propagation-of-errors method as well as two implementations of a Neyman procedure where acceptance regions are constructed based on a likelihood-ratio criterion that automatically determines whether the resulting confidence interval is one-sided or two-sided. The first Neyman procedure (due to Feldman and Cousins) neglects uncertainty in the background. In the other Neyman procedure, we account for uncertainty in the background with a parametric bootstrap method. We also construct minimum length Bayesian credibility intervals. For each method, we test for the presence of a signal based on the value of the lower endpoint of the uncertainty interval. When T_bg/T is 5 or more and the expected background is 2 or less, the Feldman Cousins method outperforms the other methods considered.

12 pages,12 tables, 10 figures. This is the final version of a manuscript that has been accepted for publication by Measurement Science and Technology

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