On Bayesian analysis of on–off measurements

2016/03/02 by Dalibor Nosek, Jana Nosková
Mathematics · Physics and Astronomy · #Artificial intelligence #Astrophysics and Cosmic Phenomena #Bayesian probability #Computer science #Mathematics #Particle physics theoretical and experimental studies #Radio Astronomy Observations and Technology #Statistics #astro-ph.IM

paper · pdf · doi:10.1016/j.nima.2016.02.094

published as Nuclear Instruments and Methods in Physics Research A 820 (2016) 23

openalex publication_date 2016/03/02 · arxiv created 2016/03/10 · arxiv updated 2016/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses
• Evaluation of three methods for calculating statistical significance when incorporating a systematic uncertainty into a test of the background-only hypothesis for a Poisson process
• Significance in gamma-ray astronomy – the Li & Ma problem in Bayesian statistics