  The galaxy Luminosity Function (LF) is a key observable for galaxy formation,
evolution studies and for cosmology. In this work, we propose a novel technique
to forward model wide-field broad-band galaxy surveys using the fast image
simulator UFig and measure the LF of galaxies in the B-band. We use Approximate
Bayesian Computation (ABC) to constrain the galaxy population model parameters
of the simulations and match data from CFHTLS. We define a number of distance
metrics between the simulated and the survey data. By exploring the parameter
space of the galaxy population model through ABC to find the set of parameters
that minimize these distance metrics, we obtain constraints on the LFs of blue
and red galaxies as a function of redshift. We find that $\mathrm{M^*}$ fades
by $\Delta \mathrm{M}^*_{\mathrm{0.1-1.0,b}} = 0.68 \pm 0.52$ and $\Delta
\mathrm{M}^*_{\mathrm{0.1-1.0,r}} = 0.54 \pm 0.48$ magnitudes between redshift
$\mathrm{z = 1}$ and $\mathrm{z = 0.1}$ for blue and red galaxies,
respectively. We also find that $\phi^*$ for blue galaxies stays roughly
constant between redshift $\mathrm{z = 0.1}$ and $\mathrm{z=1}$, while for red
galaxies it decreases by $\sim 35\%$. We compare our results to other
measurements, finding good agreement at all redshifts, for both blue and red
galaxies. To further test our results, we compare the redshift distributions
for survey and simulated data. We use the spectroscopic redshift distribution
from the VIMOS Public Extragalactic Redshift Survey (VIPERS) and we apply the
same selection in colours and magnitudes on our simulations. We find a good
agreement between the survey and the simulated redshift distributions. We
provide best-fit values and uncertainties for the parameters of the LF. This
work offers excellent prospects for measuring other galaxy population
properties as a function of redshift using ABC.
