  In the hadronic fireball phenomenology of Gamma Ray Bursts (GRBs), it is
expected that the observed photons are accompanied by UHE neutrinos, which have
not been observed yet. It is one of the challenges of experimental UHE neutrino
astrophysics to look for a signal from GRBs. In this paper, the differences
between a search for a diffuse signal and an examination of a source sample
given by e.g. BATSE will be analyzed. Since redshift information is needed to
determine the correct energy spectrum, long duration bursts with redshifts from
different estimate methods will be used. We will start with an overview of the
current understanding of GRB neutrino physics and will then use this knowledge
to make predictions for a coincidence flux and a corresponding diffuse flux. It
can be shown that shape and normalization of the spectrum is highly dependent
on the set of bursts used and that individual bursts can determine the total
spectrum.
