Tests of Statistical Significance and Background Estimation in Gamma Ray Air Shower Experiments

In this paper we discuss several methods of significance calculation and point out the limits of their applicability. We then introduce a self consistent scheme for source detection and discuss some of its properties. The method allows incorporating background anisotropies by vetoing existing small scale regions on the sky and compensating for known large scale anisotropies. By giving an example using Milagro gamma ray observatory we demonstrate how the method can be employed to relax the detector stability assumption. Two practical implementations of the method are discussed. The method is universal and can be used with any large field-of-view detector, where the object of investigation, steady or transient, point or extended, traverses its field of view.