Redshift inference from the combination of galaxy colors and clustering in a hierarchical Bayesian model

TL;DR

This paper introduces a hierarchical Bayesian framework that combines galaxy colors and clustering data to improve redshift estimates, reducing uncertainties and biases for cosmological studies.

Contribution

The novel hierarchical Bayesian model integrates photometric and clustering data for the first time, providing full posterior distributions of galaxy redshifts.

Findings

Clustering information tightens redshift posteriors.

Method reduces biases in redshift estimation.

Enables propagation of redshift uncertainties into cosmology.

Abstract

Powerful current and future cosmological constraints using high precision measurements of the large-scale structure of galaxies and its weak gravitational lensing effects rely on accurate characterization of the redshift distributions of the galaxy samples using only broadband imaging. We present a framework for constraining both the redshift probability distributions of galaxy populations and the redshifts of their individual members. We use a hierarchical Bayesian model (HBM) which provides full posterior distributions on those redshift probability distributions, and, for the first time, we show how to combine survey photometry of single galaxies and the information contained in the galaxy clustering against a well-characterized tracer population in a robust way. One critical approximation turns the HBM into a system amenable to efficient Gibbs sampling. We show that in the absence of photometric information, this method reduces to commonly used clustering redshift estimators. Using a simple model system, we show how the incorporation of clustering information with photo-$z$'s tightens redshift posteriors, and can overcome biases or gaps in the coverage of a spectroscopic prior. The method enables the full propagation of redshift uncertainties into cosmological analyses, and uses all the information at hand to reduce those uncertainties and associated potential biases.