Dark Energy Survey Year 3 results: Marginalisation over redshift distribution uncertainties using ranking of discrete realisations

Abstract

Cosmological information from weak lensing surveys is maximised by dividing source galaxies into tomographic sub-samples for which the redshift distributions are estimated. Uncertainties on these redshift distributions must be correctly propagated into the cosmological results. We present hyperrank, a new method for marginalising over redshift distribution uncertainties in cosmological analyses, using discrete samples from the space of all possible redshift distributions. This is demonstrated in contrast to previous highly simplified parametric models of the redshift distribution uncertainty. In hyperrank the set of proposed redshift distributions is ranked according to a small (in this work between one and four) number of summary values, which are then sampled along with other nuisance parameters and cosmological parameters in the Monte Carlo chain used for inference. This can be regarded as a general method for marginalising over discrete realisations of data vector variation with nuisance parameters, which can consequently be sampled separately to the main parameters of interest, allowing for increased computational efficiency. We focus on the case of weak lensing cosmic shear analyses and demonstrate our method using simulations made for the Dark Energy Survey (DES). We show the method can correctly and efficiently marginalise over a range of models for the redshift distribution uncertainty. Finally, we compare hyperrank to the common mean-shifting method of marginalising over redshift uncertainty, validating that this simpler model is sufficient for use in the DES Year 3 cosmology results presented in companion papers.

arXiv commentAccepted for publication in MNRAS. 17 pages, 12 figures, comments welcome Replacement: Added small comments suggested by referee

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• Dark Energy Survey Year 3 results: Cosmological constraints from galaxy clustering and galaxy-galaxy lensing using the MagLim lens sample
• Dark Energy Survey Year 3 results: cosmological constraints from the analysis of cosmic shear in harmonic space
• Dark Energy Survey Year 3 Results: High-precision measurement and modeling of galaxy-galaxy lensing
• Dark Energy Survey Year 3 Results: Exploiting small-scale information with lensing shear ratios
• The SRG/eROSITA All-Sky Survey: Dark Energy Survey Year 3 Weak Gravitational Lensing by eRASS1 selected Galaxy Clusters
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• Constraining the physics of star formation from CIB-cosmic shear cross-correlations
• Dark Energy Survey Year 3 Results: Constraints on cosmological parameters and galaxy bias models from galaxy clustering and galaxy-galaxy lensing using the redMaGiC sample
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• Improving Photometric Galaxy Clustering Constraints With Cross-Bin Correlations