Probability for chance coincidence of a gamma-ray burst with a galaxy on   the sky
  The nearby long GRB 060614 was not accompanied by a supernova, challenging the collapsar model for long-duration GRBs and the traditional classification scheme for GRBs. However, Cobb et al. have argued that the association of GRB 060614 and its host galaxy could be chance coincidence. In this work we calculate the probability for a GRB to be randomly coincident with a galaxy on the sky, using a galaxy luminosity function obtained from current galaxy surveys. We find that, with a magnitude limit that current telescopes can reach and an evolving galaxy luminosity function obtained from VVDS, the probability for chance coincidence of a GRB with a galaxy of redshift <1.5 is about several percent. These results agree with previous estimates based on observed galaxies. For the case of GRB 060614, the probability for it to be coincident with a z<0.125 galaxy by angular separation <0.5" is ~0.02%, indicating that the association of GRB 060614 and its host galaxy is secure. If the telescope magnitude limit is significantly improved in future, the probability for GRB-galaxy association will be considerably large, making it very problematic to identify a GRB host based only on the superposition of a GRB and a galaxy on the sky. 
Maria Angela Campisi, Li-Xin Li