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The galaxy Luminosity Function (LF) is a key observable for galaxy formation,evolution studies and for cosmology. In this work, we propose a novel techniqueto forward model wide-field broad-band galaxy surveys using the fast imagesimulator UFig and measure the LF of galaxies in the B-band. We use ApproximateBayesian Computation (ABC) to constrain the galaxy population model parametersof the simulations and match data from CFHTLS. We define a number of distancemetrics between the simulated and the survey data. By exploring the parameterspace of the galaxy population model through ABC to find the set of parametersthat minimize these distance metrics, we obtain constraints on the LFs of blueand red galaxies as a function of redshift. We find that $\mathrm{M^*}$ fadesby $\Delta \mathrm{M}^*_{\mathrm{0.1-1.0,b}} = 0.68 \pm 0.52$ 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 roughlyconstant between redshift $\mathrm{z = 0.1}$ and $\mathrm{z=1}$, while for redgalaxies it decreases by $\sim 35\%$. We compare our results to othermeasurements, finding good agreement at all redshifts, for both blue and redgalaxies. To further test our results, we compare the redshift distributionsfor survey and simulated data. We use the spectroscopic redshift distributionfrom the VIMOS Public Extragalactic Redshift Survey (VIPERS) and we apply thesame selection in colours and magnitudes on our simulations. We find a goodagreement between the survey and the simulated redshift distributions. Weprovide best-fit values and uncertainties for the parameters of the LF. Thiswork offers excellent prospects for measuring other galaxy populationproperties as a function of redshift using ABC.

Measurement of the B-band Galaxy Luminosity Function with Approximate Bayesian Computation