The Milky Way dwarf spheroidal (dSph) galaxies and the Milky Way halo are considered good candidate targets for dark matter (DM) searches. In both cases the DM signature would be provided by the detection of a gamma-ray signal originated from the annihilation of DM particles. Since the possible gamma-ray signal from any given source (or sky direction) is expected to be faint, collective analyses of multiple sources (or sky directions) can enhance the sensitivity of these searches.

We have developed a model independent technique to perform the collective spectral analysis of sets of multiple gamma-ray point sources using the data collected by the Large Area Telescope onboard the Fermi satellite. The gamma-ray fluxes are reconstructed starting from the photon counts, without assuming models for both the signal and the background. Upper limits on the fluxes are evaluated with a Bayesian method and are then converted into upper limits on the DM pair annihilation cross section. We discuss the results obtained by applying this technique to a sample of 10 dwarf spheroidal galaxies and to the Milky Way dark matter halo.