On the statistical methods of the signal significance estimation in the detection of the signal from the point sources of cosmic rays

The estimation of the significance of the peaks in 1 and 2-dimensional distributions is one of the most important problems in high-energy physics and astrophysics. The physical inference from low-statistics experiments usually is biased and many discoveries lack further confirmation. We analyze the significance of the experimental evidence in the on-going efforts of detecting the point source of Cosmic Rays. The analysis is carried out in the framework of two models utilizing the extremum statistics: first - using the fixed grid of celestial coordinates, and second - using the tuned grid (introducing more degrees of freedom in the search). The test distributions for the significance estimation are obtained both from simulation models and from the analytical treatment of the problem.