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

Title: 在引力波天文学中对全分层种群后验分布进行采样

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 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. 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，对合并黑洞的分层种群后验分布进行了全面采样。 我们直接处理由所有进入GWTC-3 LIGO/Virgo/KAGRA目录的事件的二元参数（质量、自旋幅度、自旋方向、红移）组成的最相关的固有参数空间，以及源的底层种群的超参数。 这导致了一个大约500维的参数空间，与当前的研究相比，后者通过对外部单事件参数进行边缘化显著降低了目标维度。 特别是，我们可以直接访问（i）种群参数，（ii）基于种群的单事件参数，以及（iii）这两组参数之间的相关性。 我们的实现依赖于现代的概率编程语言和哈密顿蒙特卡洛方法，并对单事件后验概率进行了连续插值。 如这里所示，对完整的分层问题进行采样是可行的，并且具有优势，因为它消除了部分（但不是全部）进入似然函数的蒙特卡洛积分及其相关方差。