On the relation between frequentist and Bayesian approaches for the case of Poisson statistics

TL;DR

This paper establishes a modified frequentist approach for Poisson confidence intervals, demonstrating its equivalence to Bayesian methods with specific priors, and extends the approach to cases with nonzero background.

Contribution

It introduces a new frequentist definition for Poisson confidence intervals that aligns with Bayesian methods using a particular prior, including for nonzero background scenarios.

Findings

Modified frequentist intervals match Bayesian results with c0(b1) c0(b2) prior

Provides a unified framework for Poisson confidence intervals

Extends methodology to cases with nonzero background

Abstract

We propose modified frequentist definition for the determination of confidence intervals for the case of Poisson statistics. Namely, 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}. We also propose modified frequentist definition for the case of nonzero background.