Expected Coverage of Bayesian Confidence Intervals for the Mean of a Poisson Statistic in Measurements with Background

TL;DR

This paper evaluates the expected coverage and length of Bayesian and frequentist confidence intervals for the mean of a Poisson process with known background, providing formulas and comparisons relevant for particle physics experiments.

Contribution

It introduces formulas for calculating Bayesian confidence intervals and compares their expected coverage and length with frequentist methods under known background conditions.

Findings

Bayesian intervals' expected coverage varies with true signal and background.

Formulas enable precise calculation of Bayesian confidence intervals.

Comparison shows differences between Bayesian and frequentist interval properties.

Abstract

Expected coverage and expected length of 90% upper and lower limit and 68.27% central intervals are plotted as functions of the true signal for various values of expected background. Results for several objective priors are shown, and formulas for calculation of confidence intervals are obtained. For comparison, expected coverage and length of frequentist intervals constructed with the unified approach of Feldman and Cousins and a simple classical method are also shown. It is assumed that the expected background is accurately known prior to performing an experiment. The plots of expected coverage and length are provided for values of signal and background typical for particle experiments with small numbers of events.