Objective Bayesian analysis of "on/off" measurements

Abstract

In high-energy astrophysics, it is common practice to account for the background overlaid with the counts from the source of interest with the help of auxiliary measurements carried on by pointing off-source. In this "on/off" measurement, one knows the number of photons detected while pointing to the source, the number of photons collected while pointing away of the source, and how to estimate the background counts in the source region from the flux observed in the auxiliary measurements. For very faint sources, the number of detected photons is so low that the approximations which hold asymptotically are not valid. On the other hand, the analytical solution exists for the Bayesian statistical inference, which is valid at low and high counts. Here we illustrate the objective Bayesian solution based on the reference posterior and compare the result with the approach very recently proposed by \citet{knoetig2014}, discussing its most delicate points. In addition, we propose to compute the significance of the excess with respect to the background-only expectation with a method which is able to account for any uncertainty on the background and is valid for any photon count. This method is compared to the widely used significance formula by \citet{LiMa83}, which is based on asymptotic properties.

References in corpus (11)

• Limits and Confidence Intervals in the Presence of Nuisance Parameters
• ROOT - A C++ Framework for Petabyte Data Storage, Statistical Analysis and Visualization
• BAT - The Bayesian Analysis Toolkit
• Overall Objective Priors
• On Computing Upper Limits to Source Intensities
• Fermi observations of high-energy gamma-ray emission from GRB 080825C
• VERITAS Observations of Gamma-Ray Bursts Detected by Swift
• Plotting the Differences Between Data and Expectation
• Objective Bayes testing of Poisson versus inflated Poisson models
• Signal discovery, limits, and uncertainties with sparse On/Off measurements: an objective Bayesian analysis
• Reference analysis of the signal + background model in counting experiments II. Approximate reference prior

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