Generalized Maximum Likelihood Method for Ultrahigh Energy Cosmic Rays

The Maximum Likelihood Method is generalized to include effects important for UHECR applications. The new approach can incorporate source distance constraints implied by the observed CR energy and can allow for energy uncertainties, possible deflection in magnetic fields, multiple source types, and a spectrum of CR composition. It can be efficiently implemented and does not require the unphysical “isotropic” assumption for unidentified sources. The approach optimizes the utility of UHECR data to discriminate between source classes and can help constrain galactic and extragalactic magnetic fields. Aspects of the method are directly applicable in other contexts, such as TeV gamma ray astrophysics.