  We present a statistical framework which can be used to determine the
contribution of an unresolved population of pulsars to the gamma-ray
background. This formalism is based on the joint analysis of photon time series
over extended regions of the sky. We demonstrate the robustness of this
technique in controlled simulations of pulsar populations, and show that the
Fermi Gamma-ray Space Telescope can be used to detect a pulsar contribution as
small as 0.1% of the gamma-ray background. This technique is sensitive to
pulsar populations with photon fluxes greater than ~1E-10 cm^-2 s^-1. The
framework is extensible to arbitrarily complex searches for periodicity and can
therefore be tailored to specific applications such as all-sky surveys and
studies of the Galactic center and globular clusters.
