Maximum Likelihood method for ultrahigh energy cosmic ray cross correlations with astrophysical sources

We extend the Maximum Likelihood method used by HiRes to study cross correlations between a catalog of candidate astrophysical sources and Ultrahigh Energy Cosmic Rays (UHECRs), to allow for differing source luminosities. Our approach permits individual sources to be ranked according to their likelihood of having emitted the correlated UHECRs. We test both old and new method by simulations for various scenarios. We conclude that there are 9 true correlation between HiRes UHECRs and known BLLacs, with a 6*10^-5 probability of such a correlation arising by chance.