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 approximate to 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 modelled 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 approximate to 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, is crucial if this methodology is to be used to test hypotheses relating to the physics of galaxy formation.