Forward modeling of galaxy populations for cosmological redshift distribution inference

We present a forward modeling framework for estimating galaxy redshift distributions from photometric surveys. Our forward model is composed of: a detailed population model describing the intrinsic distribution of physical characteristics of galaxies, encoding galaxy evolution physics; a stellar population synthesis model connecting the physical properties of galaxies to their photometry; a data-model characterizing the observation and calibration processes for a given survey; and, explicit treatment of selection cuts, both into the main analysis sample and subsequent sorting into tomographic redshift bins. This approach has the appeal that it does not rely on spectroscopic calibration data, provides explicit control over modeling assumptions, and builds a direct bridge between photo-$z$ inference and galaxy evolution physics. In addition to redshift distributions, forward modeling provides a framework for drawing robust inferences about the statistical properties of the galaxy population more generally. We demonstrate the utility of forward modeling by estimating the redshift distributions for the Galaxy And Mass Assembly (GAMA) and Vimos VLT Deep (VVDS) surveys, validating against their spectroscopic redshifts. Our baseline model is able to predict tomographic redshift distributions for GAMA and VVDS with a bias of $\Delta z \lesssim 0.003$ and $\Delta z \simeq 0.01$ on the mean redshift respectively -- comfortably accurate enough for Stage III cosmological surveys -- without any hyper-parameter tuning (i.e., prior to doing any fitting to those data). We anticipate that with additional hyper-parameter fitting and modeling improvements, forward modeling can provide a path to accurate redshift distribution inference for Stage IV surveys.