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

TL;DR

This paper evaluates the coverage properties of various uncertainty interval methods for detecting weak Poisson signals amidst background noise, comparing frequentist and Bayesian approaches under different experimental conditions.

Contribution

It introduces a comprehensive comparison of confidence and credibility interval methods, including a bootstrap-enhanced Neyman procedure, for weak signal detection in Poisson processes.

Findings

Feldman-Cousins method performs best when background uncertainty is small and exposure ratio is high.

Bayesian intervals provide competitive coverage in certain scenarios.

Likelihood-ratio based Neyman procedures effectively adapt to signal presence detection.

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.