Modified frequentist determination of confidence intervals for Poisson distribution

TL;DR

This paper introduces modified frequentist methods for calculating confidence intervals in Poisson statistics, aligning them with Bayesian approaches and extending to cases with background noise.

Contribution

It presents new modified frequentist definitions for Poisson confidence intervals, connecting them with Bayesian priors and generalizing to nonzero background scenarios.

Findings

Modified frequentist intervals are equivalent to Bayesian methods with specific priors.

Proposed symmetric frequentist definition aligns with Bayesian approach with a particular prior.

Extensions to cases with nonzero background are provided.

Abstract

We propose modified frequentist definitions for the determination of confidence intervals for the case of Poisson statistics. We require that 1-\beta^{'} \geq \sum_{n=o}^{n_{obs}+k} P(n|\lambda) \geq \alpha^{'}. We show that this definition is equivalent to the Bayesian method with prior \pi(\lambda) \sim \lambda^{k}. Other generalizations are also considered. In particular, we propose modified symmetric frequentist definition which corresponds to the Bayes approach with the prior function \pi(\lambda) \sim 1/2(1 + \frac{n_{obs}}{\lambda}). Modified frequentist definitions for the case of nonzero background are proposed.