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 background-only experiment is 25 times longer than the primary experiment. We construct confidence intervals based on the standard propagation-of-errors method as well as two implementations of a Neyman procedure where acceptance regions are constructed based on a likelihood-ratio criterion which automatically determines whether the resulting confidence interval is one-sided or two-sided. We also construct Bayesian credibility intervals with a Markov Chain Monte Carlo method with very diffuse priors, and determine one-sided and two-sided credibility intervals for each realization of data and select the interval with the shorter length. For the cases studied, one of the Neyman procedures yields intervals with the best coverage properties and the highest signal detection probabilities.
Citation: Measurement Science and Technology
Pub Type: Journals
background contamination, detection of rare events, isotopic ratio analysis, low-level radiation detection, Markov Chain Monte Carlo, Neyman procedure, uncertainty analysis.