用模拟推断方法对比宇宙大尺度结构的形态统计量，发现新指标更敏感且精度更高。
Quantifying Weighted Morphological Content of Large-Scale Structures via Simulation-Based Inference
- 通过神经后验估计实现无似然推断，比较多种形态统计量的约束能力。
- 在质量选源条件下，联合统计量比功率谱提升45%以上对σ₈的约束精度。
- 新提出的加权形态量能捕捉各向异性信息，与传统方法互补性强。
我们基于Big Sobol Sequence模拟在红移z=0.5的晕数目录，采用无似然推断框架（通过神经后验估计实现），比较了大尺度结构高阶统计量——闵可夫斯基函数（MFs）与条件导数矩（CMD）——与红移空间晕功率谱多极矩（PS）的宇宙学约束能力，重点关注其对红移空间非线性和各向异性特征的敏感性。在基准Quijote宇宙学和15 h⁻¹Mpc的高斯平滑尺度下，CMD提供的约束普遍优于MFs。将MFs与CMD联合使用，相较于仅用MFs，对σ₈的精度提升27%⁺⁹%₋₅%，对Ωₘ提升26%⁺⁷%₋₅%，凸显了CMD对各向异性信息的补充价值。在匹配有效尺度（k_max≈0.16 h Mpc⁻¹）及三种晕选择条件（全晕、固定数密度、质量选源：M>3×10¹³ h⁻¹M☉）下，质量选源配置中联合统计量相较功率谱对σ₈的精度提升达45%⁺²⁰%₋₉%，对Ωₘ提升43%⁺¹⁰%₋⁷%。研究还扩展至连续参数空间与多平滑尺度下的形态测量预报分析。
原文摘要 · Abstract (English)
We perform a simulation-based forecasting analysis to compare the cosmological constraining power of higher-order summary statistics of the large-scale structure, the Minkowski Functionals (MFs) and a class weighted morphological measure known as the Conditional Moments of Derivatives (CMD), with that of the redshift-space halo power spectrum multipoles (PS), with a particular focus on their sensitivity to nonlinear and anisotropic features in redshift space. Our analysis relies on halo catalogs from the Big Sobol Sequence simulations at redshift $z=0.5$, employing a likelihood-free inference framework implemented via neural posterior estimation. At the fiducial Quijote cosmology and for a Gaussian smoothing scale of $R=15\,h^{-1}\mathrm{Mpc}$, CMD provide systematically tighter constraints than MFs. Combining MFs and CMD into a joint estimator improves the precision by $27\%^{+9\%}_{-5\%}$ for $σ_8$ and $26\%^{+7\%}_{-5\%}$ for $Ω_{\mathrm{m}}$ relative to MFs alone, highlighting the complementary anisotropy-sensitive information captured by the CMD in contrast to the scalar morphological content encapsulated by the MFs. We compare the combined statistic MFs+CMD with the PS at matched effective scales ($k_{\max}\simeq0.16\,h\,\mathrm{Mpc^{-1}}$) under three halo-selection conditions: all halos, fixed number density, and mass-selected ($M>3\times10^{13}\,h^{-1}M_\odot$). In the mass-selected configuration, the (weighted) morphological estimator outperforms the power spectrum by $45\%^{+20\%}_{-9\%}$ for $σ_8$ and $43\%^{+10\%}_{-7\%}$ for $Ω_{\mathrm{m}}$. We also extend the simulation-based forecast analysis across a continuous range of cosmological parameters and multiple smoothing scales for morphological measures.
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