Likelihood-free Forward Modeling for Cluster Weak Lensing and Cosmology. (arXiv:2109.09741v1 [astro-ph.CO])

<a href="http://arxiv.org/find/astro-ph/1/au:+Tam_S/0/1/0/all/0/1">Sut-Ieng Tam</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Umetsu_K/0/1/0/all/0/1">Keiichi Umetsu</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Amara_A/0/1/0/all/0/1">Adam Amara</a>

Likelihood-free inference provides a rigorous approach to preform Bayesian

analysis using forward simulations only. The main advantage of likelihood-free

methods is its 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 inference of the

cosmological parameters $(Omega_mathrm{m},sigma_8)$ and the mass scale of

the survey sample. Adopting an eROSITA-like selection function and a 10-percent

scatter in the observable-mass relation in a flat $Lambda$CDM cosmology with

$Omega_mathrm{m}=0.286$ and $sigma_8=0.82$, we create a synthetic catalog of

observable-selected NFW 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 $Omega_mathrm{m}$ parameter. For a weak-lensing survey

with a source density of $n_mathrm{g}=20$ arcmin$^{-2}$, we obtain posterior

constraints on $S_8=sigma_8(Omega_mathrm{m}/0.3)^{0.3}$ of $0.836 pm 0.032$

and $0.810 pm 0.019$ 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.

Likelihood-free inference provides a rigorous approach to preform Bayesian

analysis using forward simulations only. The main advantage of likelihood-free

methods is its 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 inference of the

cosmological parameters $(Omega_mathrm{m},sigma_8)$ and the mass scale of

the survey sample. Adopting an eROSITA-like selection function and a 10-percent

scatter in the observable-mass relation in a flat $Lambda$CDM cosmology with

$Omega_mathrm{m}=0.286$ and $sigma_8=0.82$, we create a synthetic catalog of

observable-selected NFW 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 $Omega_mathrm{m}$ parameter. For a weak-lensing survey

with a source density of $n_mathrm{g}=20$ arcmin$^{-2}$, we obtain posterior

constraints on $S_8=sigma_8(Omega_mathrm{m}/0.3)^{0.3}$ of $0.836 pm 0.032$

and $0.810 pm 0.019$ 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.

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