  Two recent publications have reported intriguing analyses, tentatively
suggesting that some aspects of IceCube data might be manifestations of
quantum-gravity-modified laws of propagation for neutrinos. We here propose a
strategy of data analysis which has the advantage of being applicable to
several alternative possibilities for the laws of propagation of neutrinos in a
quantum spacetime. In all scenarios here of interest one should find a
correlation between the energy of an observed neutrino and the difference
between the time of observation of that neutrino and the trigger time of a GRB.
We select accordingly some GRB-neutrino candidates among IceCube events, and
our data analysis finds a rather strong such correlation. This sort of studies
naturally lends itself to the introduction of a "false alarm probability",
which for our analysis we estimate conservatively to be of 1%. We therefore
argue that our findings should motivate a vigorous program of investigation
following the strategy here advocated.
