Reference analysis of the signal + background model in counting experiments

Abstract

The model representing two independent Poisson processes, labelled as "signal" and "background" and both contributing additively to the total number of counted events, is considered from a Bayesian point of view. This is a widely used model for the searches of rare or exotic events in presence of a background source, as for example in the searches performed by highenergy physics experiments. In the assumption of prior knowledge about the background yield, a reference prior is obtained for the signal alone and its properties are studied. Finally, the properties of the full solution, the marginal reference posterior, are illustrated with few examples.

Search fortt¯resonances in the lepton plus jets final state with ATLAS using4.7 fb−1Aad1, Abajyan2, Abbott3 et al. 2013Phys. Rev. D490420View full textAdd to dashboardCite

“…The prior is taken to be constant in the signal cross section, which in this case is an excellent approximation of the reference prior that maximizes the amount of missing information [89], as given in Ref. [90]. The Bayesian limits are in good agreement with results obtained using the CL s method [91,92].…”

A search for $t\bar{t}$ resonances with the ATLAS detector in 2.05 fb−1 of proton-proton collisions at $\sqrt{s} = 7~\mathrm{TeV}$

“…The posterior probability density is calculated using Bayes’ theorem, with a flat positive prior in the signal cross-section which is found to be a good approximation of the reference prior [64]. Systematic uncertainties are incorporated using nuisance parameters that smear the parameters of the Poisson probability in each bin.…”

Objective Bayesian analysis of counting experiments with correlated sources of background

“…Conjugate prior. The most convenient functional form for the prior density of the Poisson parameter is a Gamma function [6], i.e., the conjugate prior for a Poisson model, Poi(n|λ), . Alternatively, one could start from the prior most probable value (the Gamma mode is at (α − 1)/β for α > 1) and variance, or from the knowledge of intervals covering given prior probabilities (e.g.…”