Setting Confidence Belts

TL;DR

This paper introduces Bayesian credible belts for Poisson means and non-negative quantities, demonstrating their optimality and favorable frequentist properties in measurement and background scenarios.

Contribution

It presents a Bayesian method for constructing credible belts that are optimal and have good frequentist properties for Poisson and normal measurement models.

Findings

Credible belts are optimal within the Bayesian framework.

The belts exhibit good frequentist coverage properties.

The method applies to Poisson distributions with background and normal measurements.

Abstract

We propose using a Bayes procedure with uniform improper prior to determine credible belts for the mean of a Poisson distribution in the presence of background and for the continuous problem of measuring a non-negative quantity $\theta$ with a normally distributed measurement error. Within the Bayesian framework, these belts are optimal. The credible limits are then examined from a frequentist point of view and found to have good frequentist and conditional frequentist properties.