Modified frequentist determination of confidence intervals for Poisson distribution
arXiv:1209.6545 · doi:10.1134/S1063779613020081
Abstract
We propose modified frequentist definitions for the determination of confidence intervals for the case of Poisson statistics. We require that 1-β^{'} \geq \sum_{n=o}^{n_{obs}+k} P(n|λ) \geq α^{'}. We show that this definition is equivalent to the Bayesian method with prior π(λ) \sim λ^{k}. Other generalizations are also considered. In particular, we propose modified symmetric frequentist definition which corresponds to the Bayes approach with the prior function π(λ) \sim 1/2(1 + \frac{n_{obs}}λ). Modified frequentist definitions for the case of nonzero background are proposed.
15 pages, 3 figures. Talk given by N.V. Krasnikov at Workshop "Calculations for modern and future colliders", Dubna, July 2012, Russia