Objective Bayesian analysis of counting experiments with correlated sources of background

TL;DR

This paper presents an analytical Bayesian method for estimating signals in counting experiments with multiple, potentially correlated background sources, applicable in physics and astrophysics.

Contribution

It provides a novel analytic solution for Bayesian inference in models with multiple correlated backgrounds, extending previous methods to more complex scenarios.

Findings

Analytic Bayesian solution for multiple backgrounds

Inclusion of correlations through priors

Applicable to physics and astrophysics experiments

Abstract

Searches for faint signals in counting experiments are often encountered in particle physics and astrophysics, as well as in other fields. Many problems can be reduced to the case of a model with independent and Poisson-distributed signal and background. Often several background contributions are present at the same time, possibly correlated. We provide the analytic solution of the statistical inference problem of estimating the signal in the presence of multiple backgrounds, in the framework of objective Bayes statistics. The model can be written in the form of a product of a single Poisson distribution with a multinomial distribution. The first is related to the total number of events, whereas the latter describes the fraction of events coming from each individual source. Correlations among different backgrounds can be included in the inference problem by a suitable choice of the priors.