Bayesian inference from photometric redshift surveys

We show how to enhance the redshift accuracy of surveys consisting of tracers with highly uncertain positions along the line of sight. This increased redshift precision is achieved by imposing an isotropy and two-point correlation prior in a Bayesian analysis and is independent of the process that estimates the photometric redshift. In particular, our method can deal with arbitrary forms of redshift uncertainties for each galaxy. As a byproduct, the method also infers the three-dimensional density field, essentially super-resolving high-density regions in redshift space. Our method fully takes into account the survey mask and selection function. It uses a simplified Poissonian picture of galaxy formation, relating preferred locations of galaxies to regions of higher density in the matter field. The method quantifies the remaining uncertainties in the three-dimensional density field and the true radial locations of galaxies by generating samples that are constrained by the survey data. The exploration of this high-dimensional, non-Gaussian joint posterior is made feasible using multiple-block Metropolis–Hastings sampling. We demonstrate the performance of our implementation on a simulation containing 2 × 107 galaxies. We further demonstrate the robustness of our method to prior misspecification by application to mock observations built from a large-scale structure simulation. In this test, initial Gaussian redshift uncertainties with δz ∼ 0.03 can yield final redshift uncertainties of δzf ∼ 0.003 in high-density regions. These results bear out the promise of Bayesian analysis for upcoming photometric large-scale structure surveys with tens of millions of galaxies.