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Photometric galaxy surveys constitute a powerful cosmological probe but relyon the accurate characterization of their redshift distributions using onlybroadband imaging, and can be very sensitive to incomplete or biased priorsused for redshift calibration. S\'anchez & Bernstein (2019) presented ahierarchical Bayesian model which estimates those from the robust combinationof prior information, photometry of single galaxies and the informationcontained in the galaxy clustering against a well-characterized tracerpopulation. In this work, we extend the method so that it can be applied toreal data, developing some necessary new extensions to it, especially in thetreatment of galaxy clustering information, and we test it on realisticsimulations. After marginalizing over the mapping between the clusteringestimator and the actual density distribution of the sample galaxies, and usingprior information from a small patch of the survey, we find the incorporationof clustering information with photo-$z$'s to tighten the redshift posteriors,and to overcome biases in the prior that mimic those happening in spectroscopicsamples. The method presented here uses all the information at hand to reduceprior biases and incompleteness. Even in cases where we artificially bias thespectroscopic 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 trainingsamples would constitute a milestone for the control of redshift systematicuncertainties in future weak lensing analyses.

monthly notices of the royal astronomical society

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