Dark Energy Survey Year 1 Results: Multi-Probe Methodology and Simulated Likelihood Analyses

TL;DR

The paper develops a robust framework for a joint DES Year 1 3x2pt analysis combining cosmic shear, galaxy–galaxy lensing, and galaxy clustering in configuration space. It implements two independent modeling pipelines ( CosmoSIS and CosmoLike ) and an analytic non-Gaussian covariance, validating them with extensive simulated likelihood tests across 27 dimensions of cosmology and nuisance parameters. The authors demonstrate excellent agreement between pipelines (Δχ^2 ≤ 0.045) and show that carefully chosen angular scale cuts and marginalization over systematics keep biases well below the statistical uncertainties, establishing credible cosmological constraints from DES Y1. They validate the covariance with Gaussian and log-normal simulations and discuss the importance of independent code development for future, more complex multi-probe analyses, outlining clear paths for including non-linear modeling and additional probes. The work sets a precedent for rigorous software practices and multi-probe analyses in upcoming large surveys."

Abstract

We present the methodology for and detail the implementation of the Dark Energy Survey (DES) 3x2pt DES Year 1 (Y1) analysis, which combines configuration-space two-point statistics from three different cosmological probes: cosmic shear, galaxy-galaxy lensing, and galaxy clustering, using data from the first year of DES observations. We have developed two independent modeling pipelines and describe the code validation process. We derive expressions for analytical real-space multi-probe covariances, and describe their validation with numerical simulations. We stress-test the inference pipelines in simulated likelihood analyses that vary 6-7 cosmology parameters plus 20 nuisance parameters and precisely resemble the analysis to be presented in the DES 3x2pt analysis paper, using a variety of simulated input data vectors with varying assumptions. We find that any disagreement between pipelines leads to changes in assigned likelihood $Δχ^2 \le 0.045$ with respect to the statistical error of the DES Y1 data vector. We also find that angular binning and survey mask do not impact our analytic covariance at a significant level. We determine lower bounds on scales used for analysis of galaxy clustering (8 Mpc$~h^{-1}$) and galaxy-galaxy lensing (12 Mpc$~h^{-1}$) such that the impact of modeling uncertainties in the non-linear regime is well below statistical errors, and show that our analysis choices are robust against a variety of systematics. These tests demonstrate that we have a robust analysis pipeline that yields unbiased cosmological parameter inferences for the flagship 3x2pt DES Y1 analysis. We emphasize that the level of independent code development and subsequent code comparison as demonstrated in this paper is necessary to produce credible constraints from increasingly complex multi-probe analyses of current data.

Figures (11)

• Figure 1: Left: 1$\sigma$ and 2$\sigma$ contours show the forecast marginalized constraints on the matter density $\Omega_\mathrm{m}$ and amplitude parameter $S_8 = \sigma_8\sqrt{\Omega_\mathrm{m}/0.3}$ from simulated analyses of the DES-Y1 cosmic shear (green, dotted), galaxy clustering + galaxy--galaxy lensing (blue, dashed), and 3x2pt data vectors assuming the baseline analysis choices developed in this paper for flat $\Lambda$CDM cosmology. The black dashed lines indicate the fiducial cosmology. Right: Contours are as in the left panel, here showing $\Omega_\mathrm{m}$ vs. the dark energy equation of state parameter $w$, assuming a flat $w$CDM cosmology.
• Figure 2: Estimated redshift distributions of the redMaGiC lens galaxy sample (dashed lines) and the metacal source galaxy sample (solid lines) for the Y1KP analysis. The lens and source galaxies are split into five and four tomography bins respectively. See xcorrxcorrtechniqueredmagicpzphotoz for details.
• Figure 3: Left: Model data vectors (evaluated at the fiducial parameter point), with grey error bars indicating the statistical uncertainties of the DES-Y1 analysis. From top to bottom, the panels show the $\xi_+$, $\xi_-$, $\gamma_\mathrm{t}$, and $w$ correlation functions; within each panel, angular and tomography bins are arranged along the $x$-axis, with each group of 20 data points corresponding to the 20 angular bins for each tomography bin. Right: Fractional deviation of the data vector prediction from the two independent implementations (symbols; see text for details), using the same ordering of data points as the left panel. The grey bands show the statistical uncertainty of the DES-Y1 analysis. Within angular scale cuts of the DES-Y1 3x2pt analysis, the residual difference between these two implementations of the data vector corresponds to $\Delta \chi^2 = 0.045$.
• Figure 4: Comparion between parameter constraints obtained using two independent cosmological inference pipelines. The solid red/dashed black lines shows 1$\sigma$ and 2$\sigma$ parameter contours obtained using CosmoLike/CosmoSIS as modeling pipeline, respectively, with input data vectors generator by the same code. The dotted blue lines show the parameter contours obtained using CosmoLike as modeling pipeline, with an input data generated by CosmoSIS.
• Figure 5: Multi-probe correlation matrix for a joint data vector of cosmic shear, galaxy--galaxy lensing, and galaxy clustering including the non-Gaussian terms, with the same ordering as the data vector shown in Fig. \ref{['fig:cc1']}. The upper left triangle shows the correlation matrix obtained from 1200 lognormal realizations (see Sect. \ref{['sec:covval']} for details), the lower right shows the correlation matrix of the non-Gaussian halo model covariance (see Sect. \ref{['sec:covhm']}). We recommend a zoom factor of $\sim$ 5 to inspect structures within the matrix.