The question of exclusion region construction in new phenomenon searches has been causing considerable discussions for many years and yet no clear mathematical definition of the problem has been stated so far. In this paper we formulate the problem i
n mathematical terms and propose a solution to the problem within the framework of statistical tests. The proposed solution avoids problems of the currently used procedures.
In this paper, after a discussion of general properties of statistical tests, we present the construction of the most powerful hypothesis test for determining the existence of a new phenomenon in counting-type experiments where the observed Poisson p
rocess is subject to a Poisson distributed background with unknown mean.
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.
