Title: Sampling the full hierarchical population posterior distribution in gravitational-wave astronomy Show Chinese title

Title: 在引力波天文学中采样完整的层次化群体后验分布

Abstract: We present a full sampling of the hierarchical population posterior distribution of merging black holes using current gravitational-wave data. We directly tackle the most relevant intrinsic parameter space made of the binary parameters (masses, spin magnitudes, spin directions, redshift) of all the events entering the GWTC-3 LIGO/Virgo/KAGRA catalog, as well as the hyperparameters of the underlying population of sources. This results in a parameter space of about 500 dimensions, in contrast with current investigations where the targeted dimensionality is drastically reduced by marginalizing over all single-event parameters. In particular, we have direct access to (i) population parameters, (ii) population-informed single-event parameters, and (iii) correlations between these two sets of parameters. We quantify the fractional contribution of each event to the constraints on the population hyperparameters. Our implementation relies on modern probabilistic programming languages and Hamiltonian Monte Carlo, with a continuous interpolation of single-event posterior probabilities. Sampling the full hierarchical problem is feasible, as demonstrated here, and advantageous as it removes some (but not all) of the Monte Carlo integrations that enter the likelihood together with the related variances. Show Chinese abstract

Abstract: 我们使用当前的引力波数据，对合并黑洞的层次化群体后验分布进行了完整的采样。我们直接处理进入GWTC-3 LIGO/Virgo/KAGRA目录的所有事件的二元参数（质量、自旋大小、自旋方向、红移）以及源的基本群体的超参数所构成的相关内在参数空间。这导致参数空间大约有500维，与目前的研究形成对比，在这些研究中，通过边际化所有单次事件参数，目标维度大幅降低。特别是，我们直接访问（i）群体参数，（ii）基于群体的单次事件参数，以及（iii）这两组参数之间的相关性。我们量化每个事件对群体超参数约束的分数贡献。我们的实现依赖于现代概率编程语言和哈密顿蒙特卡洛方法，并且采用单次事件后验概率的连续插值。对整个层次问题进行采样是可行的，正如这里所展示的，而且是有优势的，因为它消除了一些（但不是全部）作为似然函数一部分的蒙特卡洛积分及其相关的方差。