Bayesian inference from photometric redshift surveys

Abstract

We show how to enhance the redshift accuracy of surveys consisting of tracers with highly uncertain positions along the line of sight. Photometric surveys with redshift uncertainty delta_z ~ 0.03 can yield final redshift uncertainties of delta_z_f ~ 0.003 in high density regions. This increased redshift precision is achieved by imposing an isotropy and 2-point correlation prior in a Bayesian analysis and is completely independent of the process that estimates the photometric redshift. 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 2.0 x 10^7 galaxies. These results bear out the promise of Bayesian analysis for upcoming photometric large scale structure surveys with tens of millions of galaxies.