  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.
