Reference analysis of the signal + background model in counting experiments

TL;DR

This paper develops a Bayesian reference prior for the signal in a Poisson counting experiment with background, providing a systematic approach to analyze rare event searches in high-energy physics.

Contribution

It introduces a reference prior for the signal component in a two-Poisson process model, enhancing Bayesian analysis in background-limited experiments.

Findings

Derived a reference prior for the signal parameter.

Analyzed properties of the marginal reference posterior.

Provided illustrative examples of the posterior analysis.

Abstract

The model representing two independent Poisson processes, labelled as "signal" and "background" and both contributing at the same time 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 some background source, as for example in the searches performed by the high-energy physics experiments. In the assumption of some 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.