Likelihood-free Forward Modeling for Cluster Weak Lensing and Cosmology

Abstract

Likelihood-free inference provides a rigorous approach to performing Bayesian analysis using forward simulations only. The main advantage of likelihood-free methods is their ability to account for complex physical processes and observational effects in forward simulations. Here we explore the potential of likelihood-free forward modeling for Bayesian cosmological inference using the redshift evolution of the cluster abundance combined with weak-lensing mass calibration. We use two complementary likelihood-free methods, namely Approximate Bayesian Computation (ABC) and Density-Estimation Likelihood-Free Inference (DELFI), to develop an analysis procedure for the inference of the cosmological parameters (Ω m , σ 8 ) and the mass scale of the survey sample. Adopting an eROSITA-like selection function and a 10% scatter in the observable–mass relation in a flat ΛCDM cosmology with Ω m = 0.286 and σ 8 = 0.82, we create a synthetic catalog of observable-selected Navarro–Frenk–White clusters in a survey area of 50 deg 2 . The stacked tangential shear profile and the number counts in redshift bins are used as summary statistics for both methods. By performing a series of forward simulations, we obtain convergent solutions for the posterior distribution from both methods. We find that ABC recovers broader posteriors than DELFI, especially for the Ω m parameter. For a weak-lensing survey with a source density of n g = 20 arcmin −2 , we obtain posterior constraints on S 8 = σ 8 Ω m / 0.3 0.3 of 0.836 ± 0.032 and 0.810 ± 0.019 from ABC and DELFI, respectively. The analysis framework developed in this study will be particularly powerful for cosmological inference with ongoing cluster cosmology programs, such as the XMM–XXL survey and the eROSITA all-sky survey, in combination with wide-field weak-lensing surveys.