  We conduct Bayesian model inferences from the observed K-band luminosity
function of galaxies in the local Universe, using the semi-analytic model (SAM)
of galaxy formation introduced in Lu et al (2011). The prior distributions for
the 14 free parameters include a large range of possible models. We find that
some of the free parameters, e.g. the characteristic scales for quenching star
formation in both high-mass and low-mass halos, are already tightly constrained
by the single data set. The posterior distribution includes the model
parameters adopted in other SAMs. By marginalising over the posterior
distribution, we make predictions that include the full inferential
uncertainties for the colour-magnitude relation, the Tully-Fisher relation, the
conditional stellar mass function of galaxies in halos of different masses, the
HI mass function, the redshift evolution of the stellar mass function of
galaxies, and the global star formation history. Using posterior predictive
checking with the available observational results, we find that the model
family (i) predicts a Tully-Fisher relation that is curved; (ii) significantly
over predicts the satellite fraction; (iii) vastly over predicts the HI mass
function; (iv) predicts high-z stellar mass functions that have too many low
mass galaxies and too few high mass ones. and (v) predicts a redshift evolution
of the stellar mass density and the star formation history that are in moderate
disagreement. These results suggest that some important processes are still
missing in the current model family and we discuss a number of possible
solutions to solve the discrepancies, such as interactions between galaxies and
dark matter halos, tidal stripping, the bimodal accretion of gas, preheating,
and a redshift-dependent initial mass function.
