Bayesian Approach for Counting Experiment Statistics applied to a Neutrino Point Source Analysis

TL;DR

This paper introduces a Bayesian, model-independent statistical method for analyzing counting experiment data, specifically applied to neutrino point source searches, providing robust upper limits even with low counts and incorporating prior information.

Contribution

It presents a Bayesian framework for counting experiments that yields full probability distributions and robust upper limits, applied to neutrino source analysis with validation against IceCube data.

Findings

Bayesian method produces consistent upper limits with frequentist approaches.

Full probability density functions for background and signal are obtained.

Method effectively incorporates prior information and handles low-count data.

Abstract

In this paper we present a model independent analysis method following Bayesian statistics to analyse data from a generic counting experiment and apply it to the search for neutrinos from point sources. We discuss a test statistic defined following a Bayesian framework that will be used in the search for a signal. In case no signal is found, we derive an upper limit without the introduction of approximations. The Bayesian approach allows us to obtain the full probability density function for both the background and the signal rate. As such, we have direct access to any signal upper limit. The upper limit derivation directly compares with a frequentist approach and is robust in the case of low-counting observations. Furthermore, it allows also to account for previous upper limits obtained by other analyses via the concept of prior information without the need of the ad hoc application of trial factors. To investigate the validity of the presented Bayesian approach, we have applied this method to the public IceCube 40-string configuration data for 10 nearby blazars and we have obtained a flux upper limit, which is in agreement with the upper limits determined via a frequentist approach. Furthermore, the upper limit obtained compares well with the previously published result of IceCube, using the same data set.