On Bayesian analysis of on-off measurements

TL;DR

This paper introduces a Bayesian analytical method for on-off measurements, providing consistent significance and credible intervals applicable to any number of observed events, validated through simulations and astronomy examples.

Contribution

It offers a new Bayesian framework for analyzing on-off data, accommodating zero events and diverse priors, enhancing statistical inference in experimental physics.

Findings

Method is applicable to any number of events, including zero.

Validated through Monte Carlo simulations.

Demonstrated on gamma-ray astronomy data.

Abstract

We propose an analytical solution to the on-off problem within the framework of Bayesian statistics. Both the statistical significance for the discovery of new phenomena and credible intervals on model parameters are presented in a consistent way. We use a large enough family of prior distributions of relevant parameters. The proposed analysis is designed to provide Bayesian solutions that can be used for any number of observed on-off events, including zero. The procedure is checked using Monte Carlo simulations. The usefulness of the method is demonstrated on examples from gamma-ray astronomy.