Bayesian approach for counting experiment statistics applied to a neutrino point source analysis

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.

Search for high-energy neutrinos from dust obscured Blazars

“…In the case that no significant signal is observed, an upper limit is determined. This method is described in [30] where it was applied to public IceCube data for 10 nearby Blazars, for which a flux upper limit was obtained. [29].…”

Can a single high-energy neutrino from gamma-ray bursts be a discovery?

“…With these GRB-neutrino rate estimates, the extended searches required for detection will also have a significant contribution from atmospheric background neutrinos. Therefore, it can be critical to use all available information about the emission process to better identify astrophysical neutrinos by improving the signal to noise ratio (see, e.g., [14,15] for improved stacking methods).…”