  Addressing the origin of the astrophysical neutrino flux observed by IceCube
is of paramount importance. Gamma-Ray Bursts (GRBs) are among the few
astrophysical sources capable of achieving the required energy to contribute to
such neutrino flux through p$\gamma$ interactions. In this work, ANTARES data
have been used to search for upward going muon neutrinos in spatial and
temporal coincidence with 784 GRBs occurred from 2007 to 2017. For each GRB,
the expected neutrino flux has been calculated in the framework of the internal
shock model and the impact of the lack of knowledge on the majority of source
redshifts and on other intrinsic parameters of the emission mechanism has been
quantified. It is found that the model parameters that set the radial distance
where shock collisions occur have the largest impact on neutrino flux
expectations. In particular, the bulk Lorentz factor of the source ejecta and
the minimum variability timescale are found to contribute significantly to the
GRB-neutrino flux uncertainty. For the selected sources, ANTARES data have been
analysed, by maximising the discovery probability of the stacking sample
through an extended maximum-likelihood strategy. Since no neutrino event passed
the quality cuts set by the optimisation procedure, 90\% confidence level upper
limits (with their uncertainty) on the total expected diffuse neutrino flux
have been derived, according to the model. The GRB contribution to the observed
diffuse astrophysical neutrino flux around 100 TeV is constrained to be less
than 10\%.
