  [abridged] We present a statistical exploration of the parameter space of the
De Lucia and Blaizot version of the Munich semi-analytic model built upon the
millennium dark matter simulation. This is achieved by applying a Monte Carlo
Markov Chain method to constrain the 6 free parameters that define the stellar
and black-hole mass functions at redshift zero. The model is tested against
three different observational data sets, including the galaxy K-band luminosity
function, B-V colours, and the black hole-bulge mass relation, separately and
combined, to obtain mean values, confidence limits and likelihood contours for
the best fit model. Using each observational data set independently, we discuss
how the SA model parameters affect each galaxy property and to what extent the
correlations between them can lead to improved understandings of the physics of
galaxy formation. When all the observations are combined, we find reasonable
agreement between the majority of the previously published parameter values and
our confidence limits. However, the need to suppress dwarf galaxy formation
requires the strength of the supernova feedback to be significantly higher in
our best-fit solution than in previous work. To balance this, we require the
feedback to become ineffective in halos of lower circular velocity than before,
so as to permit the formation of sufficient high-luminosity galaxies:
unfortunately, this leads to an excess of galaxies around L*. Although the
best-fit is formally consistent with the data, there is no region of parameter
space that reproduces the shape of galaxy luminosity function across the whole
magnitude-range. We discuss modifications to the semi-analytic model that might
simultaneously improve the fit to the observed luminosity function and reduce
the reliance on excessive supernova feedback in small halos.
