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Abstract

We present a new method to estimate redshift distributions and galaxy-dark matter bias parameters using correlation functions in a fully data driven and self-consistent manner. Unlike other machine learning, template, or correlation redshift methods, this approach does not require a reference sample with known redshifts. By measuring the projected cross- and auto-correlations of different galaxy sub-samples, e.g. as chosen by simple cells in colour–magnitude space, we are able to estimate the galaxy-dark matter bias model parameters, and the shape of the redshift distributions of each sub-sample. This method fully marginalizes over a flexible parametrization of the redshift distribution and galaxy-dark matter bias parameters of sub-samples of galaxies, and thus provides a general Bayesian framework to incorporate redshift uncertainty into the cosmological analysis in a data-driven, consistent, and reproducible manner. This result is improved by an order of magnitude by including cross-correlations with the cosmic microwave background and with galaxy–galaxy lensing. We showcase how this method could be applied to real galaxies. By using idealized data vectors, in which all galaxy-dark matter model parameters and redshift distributions are known, this method is demonstrated to recover unbiased estimates on important quantities, such as the offset Δ_z between the mean of the true and estimated redshift distribution and the 68 per cent, 95 per cent, and 99.5 per cent widths of the redshift distribution to an accuracy required by current and future surveys.