Fast and Flow-rious: 利用归一化流和嵌套采样进行引力波背景贝叶斯模型比较
Fast and Flow-rious: Gravitational Wave Background Bayesian Model Comparison using Normalizing Flows and Nested Sampling
- Oregon State University（俄勒冈州立大学）
- NASA Marshall Space Flight Center（美国国家航空航天局马歇尔太空飞行中心）
- Vanderbilt University（范德堡大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对脉冲星计时阵列引力波背景模型比较计算昂贵的问题，提出结合归一化流、嵌套采样和边缘化似然的方法，在消费级硬件上数分钟内完成任意谱模型的贝叶斯比较，AUC达0.996。
AI中文摘要：
2023年，世界各地的脉冲星计时阵列（PTA）合作组宣布发现了纳赫兹引力波背景（GWB）的证据。除了提高探测显著性之外，下一个主要目标是表征GWB并确定其来源。PTA分析中使用的典型模型比较指标是贝叶斯因子（BF）。然而，PTA文献中使用的BF计算方法，如乘积空间采样和热力学积分，在比较的模型不相似或非嵌套时，计算成本高昂或效率低下。在这项工作中，我们引入了一种PTA模型比较方法，该方法结合了归一化流、嵌套采样以及一个对所有非GWB参数边缘化的PTA似然函数。这些流使用新开发的Python包coppuccino进行训练，该包学习数据的copula：即转换为均匀边缘分布后的依赖结构。我们在解析目标和模拟PTA数据上验证了该方法，在误差棒内恢复了解析证据，并在将BF视为注入模型的二元分类器时，实现了0.996的曲线下面积（AUC）得分。结果是，在消费级硬件上，可以在几分钟内对任意GWB谱模型进行贝叶斯模型比较。
英文摘要：
In 2023, pulsar timing array (PTA) collaborations around the world announced evidence for a nanohertz gravitational-wave background (GWB). Beyond increasing the detection significance, the next major goal is to characterize the GWB and identify its source(s). The typical model-comparison metric used in PTA analyses is the Bayes factor (BF). However, BF computation methods used in the PTA literature, such as product-space sampling and thermodynamic integration, are computationally expensive or inefficient if the models compared are dissimilar or non-nested. In this work, we introduce a PTA model-comparison method using a combination of normalizing flows, nested sampling, and a PTA likelihood that is marginalized over all non-GWB parameters. The flows are trained using a newly-developed Python package coppuccino, which learns the data's copula: the dependence structure after transforming to uniform marginals. We validate the method on both analytic targets and simulated PTA data, recovering the analytic evidence within error bars and achieving an area-under-the-curve (AUC) score of 0.996 when treating the BFs as binary classifiers of the injected models. The result is a method to perform Bayesian model comparison of arbitrary GWB spectral models in minutes on consumer hardware.
