  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.
