We present a numerical code designed to conduct a likelihood analysis for
clusters of nucleons above 10**19 eV originating from discrete astrophysical
sources such as powerful radio galaxies, gamma-ray bursts or topological
defects. The code simulates the propagation of nucleons in a large-scale
magnetic field and constructs the likelihood of a given observed event cluster
as a function of the average time delay due to deflection in the magnetic
field, the source activity time scale, the total fluence of the source, and the
power law index of the particle injection spectrum. Other parameters such as
the coherence length and the power spectrum of the magnetic field are also
considered. We apply it to the three pairs of events above 4X10**19 eV recently
reported by the Akeno Giant Air Shower Array (AGASA) experiment, assuming that
these pairs were caused by nucleon primaries which originated from a common
source. Although current data are too sparse to fully constrain each of the
parameters considered, and/or to discriminate models of the origin of
ultra-high energy cosmic rays, several tendencies are indicated. If the
clustering suggested by AGASA is real, next generation experiments with their
increased exposure should detect more than 10 particles per source over a few
years and our method will put strong constraints on both the large-scale
magnetic field parameters and the nature of these sources.Comment: 11 latex pages, 8 postscript figures included, uses revtex.sty in
two-column format and epsf.sty. Submitted to Physical Review
