Improved Weak Lensing Photometric Redshift Calibration via StratLearn and Hierarchical Modeling

TL;DR

This paper introduces a Bayesian hierarchical modeling approach combined with StratLearn to improve photometric redshift calibration for cosmic shear surveys, significantly reducing biases and enhancing the accuracy of galaxy tomographic binning.

Contribution

It presents a novel combination of StratLearn and hierarchical modeling to improve photo-z calibration, outperforming previous methods in bias reduction.

Findings

Nearly unbiased estimates of population means achieved

Maximum bias per bin of 0.0095 in redshift

Approximately 2-fold improvement over previous methods

Abstract

Discrepancies between cosmological parameter estimates from cosmic shear surveys and from recent Planck cosmic microwave background measurements challenge the ability of the highly successful $\Lambda$CDM model to describe the nature of the Universe. To rule out systematic biases in cosmic shear survey analyses, accurate redshift calibration within tomographic bins is key. In this paper, we improve photo-$z$ calibration via Bayesian hierarchical modeling of full galaxy photo-$z$ conditional densities, by employing $\textit{StratLearn}$, a recently developed statistical methodology, which accounts for systematic differences in the distribution of the spectroscopic training/source set and the photometric target set. Using realistic simulations that were designed to resemble the KiDS+VIKING-450 dataset, we show that $\textit{StratLearn}$-estimated conditional densities improve the galaxy tomographic bin assignment, and that our $\textit{StratLearn}$-Bayesian framework leads to nearly unbiased estimates of the target population means. This leads to a factor of $\sim 2$ improvement upon the previously best photo-$z$ calibration method. Our approach delivers a maximum bias per tomographic bin of $\Delta \langle z \rangle = 0.0095 \pm 0.0089$, with an average absolute bias of $0.0052 \pm 0.0067$ across the five tomographic bins.