[Paper Review] Dark Energy Survey Year 1 Results: Multi-Probe Methodology and Simulated Likelihood Analyses

E. Krause, T. F. Eifler+84 more|arXiv (Cornell University)|Jun 28, 2017

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy1 references126 citations

TL;DR

This paper presents the methodology, two independent likelihood pipelines, and covariance validation for DES Y1 3x2pt analysis combining cosmic shear, galaxy–galaxy lensing, and galaxy clustering, including robust scale cuts and systematics modeling.

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.

Motivation & Objective

• Motivate and validate the likelihood framework for DES Y1 multi-probe (3x2pt) cosmology.
• Develop and compare two independent modeling pipelines to ensure robust inferences.
• Derive and validate analytical real-space multi-probe covariance matrices.
• Assess impact of scale cuts and systematics on cosmological parameter recovery.
• Demonstrate robustness of inference against a variety of systematic effects.

Proposed method

• Construct a baseline theoretical model for angular two-point functions of three probes using Limber-approximated integrals with a non-linear matter power spectrum.
• Implement two independent pipelines (CosmoSIS-based and CosmoLike-based) to compute data vectors and covariances.
• Derive analytical real-space multi-probe covariances and validate them against simulations.
• Stress-test inference through simulated likelihood analyses with 6–7 cosmological and ~20 nuisance parameters.
• Use photometric redshift, galaxy bias, shear calibration, and intrinsic alignment systematics with corresponding priors and scale-cuts.
• Adopt a joint 3x2pt data vector comprising xi_plus, xi_minus, gamma_t, and w, across tomographic bins.

Experimental results

Research questions

• RQ1 Can a dual independent modeling pipeline yield consistent cosmological inferences for DES Y1 3x2pt data?
• RQ2 How do analytic covariances perform relative to numerical simulations in a multi-probe setup?
• RQ3 What scale-cuts are required to ensure non-linear modeling uncertainties are subdominant to statistical errors?
• RQ4 How robust are DES Y1 inferences to priors and nuisance parameter modeling of photo-z, bias, shear calibration, and intrinsic alignments?
• RQ5 What is the gain in information from combining cosmic shear, galaxy–galaxy lensing, and galaxy clustering compared to individual probes?

Key findings

• Disagreement between the two pipelines yields Δχ2 ≤ 0.045 relative to the DES Y1 statistical error.
• Angular binning and survey mask do not significantly affect the analytic covariance.
• Lower scale cuts of ~8 Mpc/h for clustering and ~12 Mpc/h for galaxy–galaxy lensing keep non-linear modeling uncertainties below statistical errors.
• The joint 3x2pt analysis yields robust, unbiased cosmological parameter inferences for the DES Y1 analysis.
• Independent code development and cross-checks are essential for credible multi-probe cosmological constraints.