  We explore the parameter space of the semi-analytic galaxy formation model
GALFORM, studying the constraints imposed by measurements of the galaxy stellar
mass function (GSMF) and its evolution. We use the Bayesian Emulator method to
quickly eliminate vast implausible volumes of the parameter space and zoom in
on the most interesting regions, allowing us to identify a set of models that
match the observational data within model uncertainties. We find that the GSMF
strongly constrains parameters related to quiescent star formation in discs,
stellar and AGN feedback and threshold for disc instabilities, but weakly
restricts other parameters. Constraining the model using local data alone does
not usually select models that match the evolution of the GSMF well.
Nevertheless, we show that a small subset of models provides acceptable match
to GSMF data out to redshift 1.5. We explore the physical significance of the
parameters of these models, in particular exploring whether the model provides
a better description if the mass loading of the galactic winds generated by
starbursts ($\beta_{0,\text{burst}}$) and quiescent disks
($\beta_{0,\text{disc}}$) is different. Performing a principal component
analysis of the plausible volume of the parameter space, we write a set of
relations between parameters obeyed by plausible models with respect to GSMF
evolution. We find that while $\beta_{0,\text{disc}}$ is strongly constrained
by GSMF evolution data, constraints on $\beta_{0,\text{burst}}$ are weak.
Although it is possible to find plausible models for which
$\beta_{0,\text{burst}} = \beta_{0,\text{disc}}$, most plausible models have
$\beta_{0,\text{burst}}>\beta_{0,\text{disc}}$, implying - for these - larger
SN feedback efficiency at higher redshifts.
