  Many sources contribute to the diffuse gamma-ray background (DGRB), including
star forming galaxies, active galactic nuclei, and cosmic ray interactions in
the Milky Way. Exotic sources, such as dark matter annihilation, may also make
some contribution. The photon counts-in-pixels distribution is a powerful tool
for analyzing the DGRB and determining the relative contributions of different
sources. However, including photon energy information in a likelihood analysis
of the counts-in-pixels distribution quickly becomes computationally
intractable as the number of source types and energy bins increase. Here, we
apply the likelihood-free method of Approximate Bayesian Computation (ABC) to
the problem. We consider a mock analysis that includes contributions from dark
matter annihilation in galactic subhalos as well as astrophysical backgrounds.
We show that our results using ABC are consistent with the exact likelihood
when energy information is discarded, and that significantly tighter parameter
constraints can be obtained with ABC when energy information is included. ABC
presents a powerful tool for analyzing the DGRB and understanding its varied
origins.
