  This paper treats the problem of detecting periodicity in a sequence of
photon arrival times, which occurs, for example, in attempting to detect
gamma-ray pulsars. A particular focus is on how auxiliary information,
typically source intensity, background intensity, and incidence angles and
energies associated with each photon arrival should be used to maximize the
detection power. We construct a class of likelihood-based tests, score tests,
which give rise to event weighting in a principled and natural way, and derive
expressions quantifying the power of the tests. These results can be used to
compare the efficacies of different weight functions, including cuts in energy
and incidence angle. The test is targeted toward a template for the periodic
lightcurve, and we quantify how deviation from that template affects the power
of detection.
