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 sorting source galaxies into tomographic redshift subsamples. Any uncertainties on these redshift distributions must be correctly propagated into the cosmological results. We present , a new method for marginalising over redshift distribution uncertainties, using discrete samples from the space of all possible redshift distributions, improving over simple parameterized models. In the set of proposed redshift distributions is ranked according to a small (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 approach 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 from 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 wide range of models for the redshift distribution uncertainty. Finally, we compare 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.

Dark Energy Survey Year 3 results: Cosmology from cosmic shear and robustness to modeling uncertainty

“…(v) The characterization of the source redshift distribution, and the related systematic and statistical uncertainties, are detailed in five papers. Namely, Myles et al [79] and Buchs et al [55] present the baseline methodology for estimating wide-field redshift distributions using Self-Organizing Maps; Gatti et al [80] outline an alternative method using cross correlations with spectroscopic galaxies; Sánchez et al [81] presents a complementary likelihood using small scale galaxy-galaxy lensing, improving constraints on redshifts and IA; finally Cordero et al [82] validates our fiducial error parametrization using a more complete alternative based on distribution realizations. In addition to this, Hartley et al [83] and Everett et al [84] respectively describe the DES deep fields and the Balrog image simulations, both of which are crucial in testing and implementing the Y3 redshift methodology.…”

Dark Energy Survey Y3 results: blending shear and redshift biases in image simulations

“…This procedure results in a set of n γ (z) samples, which can be sampled over when performing cosmological parameter inference (e.g. using the HYPERRANK method described in Cordero et al 2021).…”

“…shear correlation functions or tangential shear) for the DES Year 3 shear catalogue. An algorithm for efficiently sampling over discrete n γ (z) samples, such as that presented in Cordero et al (2021) can be used (or alternatively one could directly sample the likelihood in equation 35, simultaneously with the likelihood for the Year 3 weak lensing statistics). However, for some applications, it may be desirable and sufficiently accurate to directly use the inferred m and δ z statistics as approximate corrections to the effective redshift distribution, and sample over them as nuisance parameters.…”

Dark Energy Survey Year 3 Results: clustering redshifts – calibration of the weak lensing source redshift distributions with redMaGiC and BOSS/eBOSS

“…An additional correction to all the n ( z) realizations is performed to account for the effects of blending, based on the work on image simulations described in MacCrann et al ( 2022 ). Then, ideally, the realizations are sampled o v er during the cosmological analysis, using the hyperr ank technique (Cordero et al 2021 ). In practice, ho we ver, in our fiducial cosmological run, we decided to parametrize the n ( z) uncertainties by shifts around their mean with a shift parameter z.…”

“…In practice, ho we ver, in our fiducial cosmological run, we decided to parametrize the n ( z) uncertainties by shifts around their mean with a shift parameter z. This choice was dictated by efficiency reasons, and by the fact that we verified in Cordero et al ( 2021 ) that marginalizing o v er the mean of the redshift distributions rather than sampling o v er the multiple n ( z) realizations was sufficient for the DES Y3 analysis. The prior on z is naturally provided by the scatter on the mean of the n ( z) realizations.…”