Dwarf galaxies are known to have remarkably low star formation efficiency due to strong feedback. Adopting the dwarf galaxies of the Milky Way as a laboratory, we explore a flexible semi-analytic galaxy formation model to understand how the feedback processes shape the satellite galaxies of the Milky Way. Using Markov-Chain Monte-Carlo, we exhaustively search a large parameter space of the model and rigorously show that the general wisdom of strong outflows as the primary feedback mechanism cannot simultaneously explain the stellar mass function and the mass--metallicity relation of the Milky Way satellites. An extended model that assumes that a fraction of baryons is prevented from collapsing into low-mass halos in the first place can be accurately constrained to simultaneously reproduce those observations. The inference suggests that two different physical mechanisms are needed to explain the two different data sets. In particular, moderate outflows with weak halo mass dependence are needed to explain the mass--metallicity relation, and prevention of baryons falling into shallow gravitational potentials of low-mass halos (e.g. pre-heating) is needed to explain the low stellar mass fraction for a given subhalo mass.
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