Redshift inference from the combination of galaxy colors and clustering in a hierarchical Bayesian model – Application to realistic N-body simulations

Photometric galaxy surveys constitute a powerful cosmological probe but rely on the accurate characterization of their redshift distributions using only broadband imaging, and can be very sensitive to incomplete or biased priors used for redshift calibration. S\'anchez & Bernstein (2019) presented a hierarchical Bayesian model which estimates those from the robust combination of prior information, photometry of single galaxies and the information contained in the galaxy clustering against a well-characterized tracer population. In this work, we extend the method so that it can be applied to real data, developing some necessary new extensions to it, especially in the treatment of galaxy clustering information, and we test it on realistic simulations. After marginalizing over the mapping between the clustering estimator and the actual density distribution of the sample galaxies, and using prior information from a small patch of the survey, we find the incorporation of clustering information with photo-$z$'s to tighten the redshift posteriors, and to overcome biases in the prior that mimic those happening in spectroscopic samples. The method presented here uses all the information at hand to reduce prior biases and incompleteness. Even in cases where we artificially bias the spectroscopic sample to induce a shift in mean redshift of $\Delta \bar z \approx 0.05,$ the final biases in the posterior are $\Delta \bar z \lesssim0.003.$ This robustness to flaws in the redshift prior or training samples would constitute a milestone for the control of redshift systematic uncertainties in future weak lensing analyses.