AI 中文总结
本研究在爱因斯坦望远镜时代对比分层贝叶斯推断（HBI）与基于模拟的推断（SBI），发现SBI可高精度复现HBI结果且计算量更低，还能便捷扩展至联合分析，是适用于第三代引力波探测器种群推断的可扩展工具。
AI 中文摘要
下一代引力波探测器（如爱因斯坦望远镜，ET）将观测到比当前设备多几个数量级的双黑洞并合事件，其中多数事件将缺乏电磁对应体，即所谓的“暗哨事件”，但仍能实现百分级的宇宙学约束。然而，用于种群水平分析的分层贝叶斯推断（HBI）中传统的似然函数，会随着暗哨事件星表规模和种群参数的增长而变得计算上不可行。本研究在爱因斯坦望远镜时代，将HBI与作为可扩展替代方案的基于模拟的推断（SBI）进行比较，用于宇宙学种群推断。通过对模拟ET推断的概念验证示例进行研究，我们构建了包含约10^4个双黑洞事件的星表，分别使用分层分析似然函数和边际神经比估计（MNRE），对平坦ΛCDM宇宙学中的哈勃常数H₀和物质密度Ωₘ进行推断。我们发现两种方法的结果吻合度极高，SBI能以高精度复现HBI的后验分布，且在分摊模拟与训练成本后，所需计算量减少几个数量级。我们进一步证明，SBI可直接扩展至宇宙学-天体物理学联合分析，在几乎不增加额外成本的情况下，同时约束(H₀,Ωₘ)与恒星形成率密度的参数，而在HBI框架内实现此类扩展则需要显著提升复杂度。研究结果表明，SBI是适用于第三代引力波探测器种群推断的有前景且可扩展的工具。
英文摘要
The next generation of gravitational wave detectors, such as the Einstein Telescope (ET), will observe orders of magnitude more binary black hole mergers than current facilities. Most of these events will lack an electromagnetic counterpart, also known as dark siren events, yet will still enable percent-level cosmological constraints. However, the likelihood traditionally used in Hierarchical Bayesian Inference (HBI) for population-level analyses becomes computationally prohibitive as the size of dark siren catalogues and population parameters grow. In this work we compare HBI against simulation-based inference (SBI) as a scalable alternative for cosmological population inference in the ET era. Studying a proof-of-concept example of a mock ET inference, we build a catalogue of $O(10^4)$ binary black hole events, then perform inference on the Hubble constant $H_0$ and matter density $Ω_m$ in a flat $Λ$CDM cosmology, using both a hierarchical analytical likelihood and Marginal Neural Ratio Estimation (MNRE). We find excellent agreement between the two approaches, with SBI reproducing the HBI posteriors to high accuracy, while requiring orders of magnitude less computation once the simulation and training cost is amortized. We further demonstrate that SBI extends straightforwardly to a joint cosmology-plus-astrophysics analysis, simultaneously constraining $(H_0,Ω_m)$ together with the parameters of the star formation rate density, at negligible additional cost compared to the significant increase in complexity such an extension would require within the HBI framework. Our results indicate that SBI is a promising and scalable tool for population inference with third-generation GW detectors.
Comments28 pages, 8 figures. Links to codes: Sireeni: https://github.com/GFAbellan/Sireeni, darksirens_hbi: https://gitlab.com/gantinoz/darksirens_hbi
