emuflow：用于联合宇宙学分析的正则化流
$\mathtt{emuflow}$: Normalising Flows for Joint Cosmological Analysis
AI总结：
本文提出利用正则化流模拟边缘后验分布，从而在不增加参数空间维度的情况下高效结合多个宇宙学数据集的约束，显著降低计算成本，并公开了模型与软件。
摘要：
鉴于宇宙学研究所关注的天文数据集在种类和精度上的不断增长，最佳的宇宙学约束往往是通过结合不同实验的数据来获得的。在似然层面进行这种结合时，一个复杂之处在于需要对描述每个实验数据的大维度参数模型进行边缘化。这些参数既包括数量相对较少的宇宙学兴趣参数，也包括大量的“ nuisance ”参数。因此，在多个实验的联合参数空间中进行采样可能成为一项计算成本极高的操作。如果能够直接从先前实验的边缘宇宙学后验分布中采样，并且该分布仅依赖于共同的宇宙学参数集合，那么这一过程就可以得到显著简化。在本文中，我们展示了可以通过正则化流来模拟边缘后验分布，从而实现这一目标。训练得到的正则化流模型可用于高效地结合来自独立数据集的宇宙学约束，而不会增加所研究参数空间的维度。我们证明，该方法能够准确描述真实宇宙学数据集的后验分布，以及不同数据集的联合分布，即使在实验之间存在显著张力的情况下也是如此。由此得到的联合约束可以在远少于在似然层面结合相同数据集所需的时间内获得。我们为一组具有普遍兴趣的公开宇宙学数据集构建了正则化流模型，并将其与用于训练这些模型的软件以及用于在宇宙学参数推断中利用这些模型的软件一起公开提供。
英文摘要：
Given the growth in the variety and precision of astronomical datasets of interest for cosmology, the best cosmological constraints are invariably obtained by combining data from different experiments. At the likelihood level, one complication in doing so is the need to marginalise over large-dimensional parameter models describing the data of each experiment. These include both the relatively small number of cosmological parameters of interest and a large number of "nuisance" parameters. Sampling over the joint parameter space for multiple experiments can thus become a very computationally expensive operation. This can be significantly simplified if one could sample directly from the marginal cosmological posterior distribution of preceding experiments, depending only on the common set of cosmological parameters. In this paper, we show that this can be achieved by emulating marginal posterior distributions via normalising flows. The resulting trained normalising flow models can be used to efficiently combine cosmological constraints from independent datasets without increasing the dimensionality of the parameter space under study. We show that the method is able to accurately describe the posterior distribution of real cosmological datasets, as well as the joint distribution of different datasets, even when significant tension exists between experiments. The resulting joint constraints can be obtained in a fraction of the time it would take to combine the same datasets at the level of their likelihoods. We construct normalising flow models for a set of public cosmological datasets of general interests and make them available, together with the software used to train them, and to exploit them in cosmological parameter inference.
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