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arXiv 2109.09741astro-ph.COastro-ph.GA
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团簇弱透镜和宇宙学的无似然正演模拟

Likelihood-free Forward Modeling for Cluster Weak Lensing and Cosmology

Sut-Ieng Tam, Keiichi Umetsu, Adam Amara

摘要:

似然自由推理提供了一种严格的方法来执行贝叶斯分析,只使用正向模拟。无似然方法的主要优点是它能够在正演模拟中考虑复杂的物理过程和观测效应。在这里,我们探讨了贝叶斯宇宙学推断的可能性无前向建模的红移演化的集群丰度结合弱透镜质量校准。我们使用两个互补的似然自由的方法,即近似贝叶斯计算(ABC)和密度估计似然自由推断(DELFI),开发的宇宙学参数$(Ω_\mathrm{m},σ_8)$和调查样本的质量规模的推断分析程序。采用类eROSITA的选择函数和10%的分散在一个平坦的$Λ$ CDM宇宙学与$Ω_\mathrm{m}=0.286$和$σ_8=0.82$的可观测质量的关系,我们创建了一个综合目录的可观测选择的NFW集团在50度的调查区域$^2$。堆叠切向剪切轮廓和红移箱中的数量计数被用作两种方法的汇总统计量。通过一系列的前向模拟,我们得到收敛的解决方案后验分布从这两种方法。我们发现,ABC恢复更广泛的后验比DELFI,特别是对于$Ω_\mathrm{m}$参数。对于源密度为$n_\mathrm{g}=20$ arcmin $^{-2}$的弱透镜观测,我们分别从ABC和DELFI得到了$0.836 \pm 0.032$和$0.810 \pm 0.019$对$S_8=σ_8(Ω_\mathrm{m}/0.3)^{0.3}$的后验约束.在这项研究中开发的分析框架将是特别强大的宇宙学推断与正在进行的集群宇宙学计划,如XMM-XXL调查和eROSITA全天空调查,结合宽场弱透镜调查。

英文摘要:

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 $(Ω_\mathrm{m},σ_8)$ 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 $Λ$CDM cosmology with $Ω_\mathrm{m}=0.286$ and $σ_8=0.82$, 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 $Ω_\mathrm{m}$ parameter. For a weak-lensing survey with a source density of $n_\mathrm{g}=20$ arcmin$^{-2}$, we obtain posterior constraints on $S_8=σ_8(Ω_\mathrm{m}/0.3)^{0.3}$ 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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