使用后验重分区和 $β$-flows 加速引力波的嵌套采样
Accelerated nested sampling with posterior repartitioning and $β$-flows for gravitational waves
AI总结：
针对引力波分析中嵌套采样计算成本高的问题，提出基于后验重分区与 $β$-flows 的加速方法，在保证后验与证据恢复精度的同时，将似然评估次数降低高达一个数量级。
AI中文摘要：
引力波社区对快速可靠的推断方法的需求日益增长，并要求伴随提供信息量的误差条。嵌套采样满足后两个要求，但在使用最精确的波形模型时，其计算成本可能变得令人望而却步。在本文中，我们展示了使用一种称为后验重分区的技术来加速嵌套采样。该方法利用嵌套采样在算法层面分离先验和似然贡献的独特能力。具体而言，我们定义了一个由低分辨率运行的后验所提供信息的“重分区先验”。为了构建这种重分区先验，我们使用了 $β$-flow，这是一种新型条件归一化流，旨在更好地学习深尾概率。$β$-flows 在整个嵌套采样运行中进行训练，并以逆温度 $β$ 为条件。将我们的方法应用于模拟和真实的双黑洞合并，我们展示了它们如何能将给定证据精度所需的似然评估次数减少高达一个数量级，从而实现更快的模型比较和参数估计。此外，我们强调了在后验重分区中使用 $β$-flows 相较于标准归一化流的鲁棒性。值得注意的是，$β$-flows 能够恢复后验和证据，这些结果通常与传统嵌套采样获得的结果一致，即使在标准归一化流失败的情况下也是如此。
英文摘要：
There is an ever-growing need in the gravitational wave community for fast and reliable inference methods, accompanied by an informative error bar. Nested sampling satisfies the last two requirements, but its computational cost can become prohibitive when using the most accurate waveform models. In this paper, we demonstrate the acceleration of nested sampling using a technique called posterior repartitioning. This method leverages nested sampling's unique ability to separate prior and likelihood contributions at the algorithmic level. Specifically, we define a `repartitioned prior' informed by the posterior from a low-resolution run. To construct this repartitioned prior, we use a $β$-flow, a novel type of conditional normalizing flow designed to better learn deep tail probabilities. $β$-flows are trained on the entire nested sampling run and conditioned on an inverse temperature $β$. Applying our methods to simulated and real binary black hole mergers, we demonstrate how they can reduce the number of likelihood evaluations required for a given evidence precision by up to an order of magnitude, enabling faster model comparison and parameter estimation. Furthermore, we highlight the robustness of using $β$-flows over standard normalizing flows for posterior repartitioning. Notably, $β$-flows are able to recover posteriors and evidences which are generally consistent with those from traditional nested sampling, even in cases where standard normalizing flows fail.
