Bayesian Approach for a Neutrino Point Source Analysis

In this paper we present a model independent analysis method following Bayesian statistics to search for neutrinos from point sources. The Bayesian approach allows us to obtain the full probability distribution function for both the background and the signal rate. As such, we have direct access to the signal significance and upper limits. Furthemore, it allows also to account for previous results via the concept of prior information without the need of the ad hoc application of trial factors. In this paper we derive an exact analytical expression for the probability density function for the source rate, and consequently also for the flux, of any steady point source assuming a uniform prior distribution. To investigate the validity of our Bayesian approach, we have applied this method to the public IceCube 40-string configuration data for 10 nearby blazars and have obtained a flux upper limit, which compares very well with the previously published result of IceCube, using the same data set.