Dwarf satellite galaxies are powerful cosmological probes because they inhabit low-mass dark matter halos and trace the hierarchical growth of structure on non-linear scales, making them sensitive to dark matter microphysics. However, much of the cosmological work with dwarf satellites thus far has focused only on satellites of the Milky Way (MW). This is due in large part to the observational challenge of detecting satellites of extragalactic hosts, but the advent of wide-field cameras on large-aperture telescopes has made such surveys viable. There is much to be gained from expanding cosmological analyses with dwarf galaxies outside the MW, but such analyses introduce new challenges on both the observational and theoretical fronts. I will discuss my work on the LBT-SONG and MADCASH surveys, which are conducting extragalactic satellite surveys on 8m-class telescopes with data quality similar to that expected from LSST. On the theoretical side, I will present results from my semi-empirical model which relates observational quantities of an observed galaxy (e.g., luminosity) to theoretical quantities (e.g., halo mass) through a joint probability distribution. This formalism is flexible, extensible, and computationally cheap, making it viable for application to next generation surveys like LSST. I will also highlight the need to understand how complete the survey is across the multi-dimensional space of dwarf properties and how I measured the completeness of LBT-SONG using image simulations and a novel catalog-based emulator.
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