Fermi-LAT observations have strongly constrained dark matter annihilation through the joint-likelihood analysis of dwarf spheroidal galaxies (dSphs). These constraints are expected to be robust because dSphs have measurable dark matter content and produce negligible astrophysical emission. However, each dSph is dim, with a predicted flux that typically falls below the accuracy of the background model. We show that this significantly diminishes the reliability of previous joint-likelihood algorithms, and develop an improved analysis that directly accounts for the effect of background mismodeling. This method produces more robust limits and detections of dark matter in both real and mock data. We calculate improved limits on the dark matter annihilation cross-section, which differ by nearly a factor of two from previous analyses - despite examining identical data.
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