High energy neutrinos

In this paper we compare the results of the MACRO detector at Gran Sasso, that is the largest neutrino telescope operated before the year 2k, with theoretical predictions of the neutrino emission from some promising targets, such as blazars and GRB's. In particular we propose a new statistical method, justified by the maximum entropy principle, for assessing a model independent upper limit to the differential flux of neutrinos inferred from the measured up-ward going muon flux. This comparison confirms that the acceptance of a detector of up-ward going muons should be of the order of $1 \mathrm{km}^2$, in order to challenge the present theoretical estimates of possible neutrino production in both galactic and extra-galactic objects.