Probing the sparse tails of redshift distributions with Voronoi tessellations

We introduce an empirical galaxy photometric redshift algorithm based upon the Voronoi tessellation density estimator in the space of redshift and photometric parameters. Our aim is to use sparse survey datasets to estimate the full shape of the redshift distribution that is defined by the degeneracies in galaxy photometric properties and redshift. We describe the algorithm implementation and provide a proof of concept using the first public data release from the VIMOS Public Extragalactic Redshift Survey (VIPERS PDR-1). We validate the method by comparing against the standard empirical redshift distribution code Trees for Photo-Z (TPZ) on both mock and real data. We find that the Voronoi tessellation algorithm accurately recovers the full shape of the redshift distribution quantified by its second moment and inferred redshift confidence intervals. The analysis allows us to properly account for galaxies in the tails of the distributions that would otherwise be classified as catastrophic outliers. The source code is publicly available at http://bitbucket.org/bengranett/tailz.