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Determining the redshift distribution $n(z)$ of galaxy samples is essentialfor several cosmological probes including weak lensing. For imaging surveys,this is usually done using photometric redshifts estimated on anobject-by-object basis. We present a new approach for directly measuring theglobal $n(z)$ of cosmological galaxy samples, including uncertainties, usingforward modeling. Our method relies on image simulations produced using UFig(Ultra Fast Image Generator) and on ABC (Approximate Bayesian Computation)within the $MCCL$ (Monte-Carlo Control Loops) framework. The galaxy populationis modeled using parametric forms for the luminosity functions, spectral energydistributions, sizes and radial profiles of both blue and red galaxies. Weapply exactly the same analysis to the real data and to the simulated images,which also include instrumental and observational effects. By adjusting theparameters of the simulations, we derive a set of acceptable models that arestatistically consistent with the data. We then apply the same cuts to thesimulations that were used to construct the target galaxy sample in the realdata. The redshifts of the galaxies in the resulting simulated samples yield aset of $n(z)$ distributions for the acceptable models. We demonstrate themethod by determining $n(z)$ for a cosmic shear like galaxy sample from the4-band Subaru Suprime-Cam data in the COSMOS field. We also complement thisimaging data with a spectroscopic calibration sample from the VVDS survey. Wecompare our resulting posterior $n(z)$ distributions to the one derived fromphotometric redshifts estimated using 36 photometric bands in COSMOS and findgood agreement. This offers good prospects for applying our approach to currentand future large imaging surveys.

The redshift distribution of cosmological samples: a forward modeling approach