  We infer mechanisms of galaxy formation for a broad family of semi-analytic
models (SAMs) constrained by the K-band luminosity function and HI mass
function of local galaxies using tools of Bayesian analysis. Even with a broad
search in parameter space the whole model family fails to match to constraining
data. In the best fitting models, the star formation and feedback parameters in
low-mass haloes are tightly constrained by the two data sets, and the analysis
reveals several generic failures of models that similarly apply to other
existing SAMs. First, based on the assumption that baryon accretion follows the
dark matter accretion, large mass-loading factors are required for haloes with
circular velocities lower than 200 km/s, and most of the wind mass must be
expelled from the haloes. Second, assuming that the feedback is powered by
Type-II supernovae with a Chabrier IMF, the outflow requires more than 25% of
the available SN kinetic energy. Finally, the posterior predictive
distributions for the star formation history are dramatically inconsistent with
observations for masses similar to or smaller than the Milky-Way mass. The
inferences suggest that the current model family is still missing some key
physical processes that regulate the gas accretion and star formation in
galaxies with masses below that of the Milky Way.
