Building a Predictive Model of Galaxy Formation - I: Phenomenological
  Model Constrained to the $z=0$ Stellar Mass Function
  We constrain a highly simplified semi-analytic model of galaxy formation
using the $z\approx 0$ stellar mass function of galaxies. Particular attention
is paid to assessing the role of random and systematic errors in the
determination of stellar masses, to systematic uncertainties in the model, and
to correlations between bins in the measured and modeled stellar mass
functions, in order to construct a realistic likelihood function. We derive
constraints on model parameters and explore which aspects of the observational
data constrain particular parameter combinations. We find that our model, once
constrained, provides a remarkable match to the measured evolution of the
stellar mass function to $z=1$, although fails dramatically to match the local
galaxy HI mass function. Several "nuisance parameters" contribute significantly
to uncertainties in model predictions. In particular, systematic errors in
stellar mass estimate are the dominant source of uncertainty in model
predictions at $z\approx 1$, with additional, non-negligble contributions
arising from systematic uncertainties in halo mass functions and the residual
uncertainties in cosmological parameters. Ignoring any of these sources of
uncertainties could lead to viable models being erroneously ruled out.
Additionally, we demonstrate that ignoring the significant covariance between
bins the observed stellar mass function leads to significant biases in the
constraints derived on model parameters. Careful treatment of systematic and
random errors in the constraining data, and in the model being constrained, are
crucial if this methodology is to be used to test hypotheses relating to the
physics of galaxy formation.
