利用归一化流从后验样本估计贝叶斯证据
Bayesian evidence estimation from posterior samples with normalizing flows
- SISSA（国际高等研究学院）
- INFN Sezione di Trieste（的里雅斯特国家核物理研究所）
- IFPU - Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）
- TAPIR, Division of Physics, Mathematics, and Astronomy, California Institute of Technology（加州理工学院）
- Dipartimento di Fisica, Università di Pisa（比萨大学）
- Department of Physics, Imperial College London（帝国理工学院）
- Italian Research Center on High Performance Computing, Big Data and Quantum Computing（意大利高性能计算、大数据与量子计算研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出基于归一化流的$floZ$方法，从已有未归一化后验样本估计贝叶斯证据及不确定性，在高维尖锐后验上更鲁棒，并成功用于GW150914铃宕泛音分析。
AI中文摘要：
我们提出了一种基于归一化流的新方法（$floZ$），用于从预先存在的、抽自未归一化后验分布的一组样本估计贝叶斯证据（及其数值不确定性）。我们在证据可解析获知的分布上对其进行了验证，参数空间维度最高达15维，并与两种最先进的证据估计技术进行了比较：嵌套采样（nested sampling，其将证据作为主要目标进行计算）和一种从后验样本生成证据估计的$k$-近邻技术。只要能够获得来自目标后验的具有代表性的样本，我们的方法对具有尖锐特征的后验分布更具鲁棒性，尤其是在更高维度下。对于简单的多元高斯分布，我们使用$10^5$个后验样本证明了其在最高200维时的准确性。$floZ$具有广泛的适用性，例如可从变分推断、马尔可夫链蒙特卡洛样本，或任何其他能够提供来自未归一化后验密度的样本及其似然的方法来估计证据。作为一项物理应用，我们使用$floZ$计算GW150914引力波数据铃宕信号中存在第一泛音的贝叶斯因子，发现其与嵌套采样结果高度一致。
英文摘要：
We propose a novel method ($floZ$), based on normalizing flows, to estimate the Bayesian evidence (and its numerical uncertainty) from a pre-existing set of samples drawn from the unnormalized posterior distribution. We validate it on distributions whose evidence is known analytically, up to 15 parameter space dimensions, and compare with two state-of-the-art techniques for estimating the evidence: nested sampling (which computes the evidence as its main target) and a $k$-nearest-neighbors technique that produces evidence estimates from posterior samples. Provided representative samples from the target posterior are available, our method is more robust to posterior distributions with sharp features, especially in higher dimensions. For a simple multivariate Gaussian, we demonstrate its accuracy for up to 200 dimensions with $10^5$ posterior samples. $floZ$ has wide applicability, e.g., to estimate evidence from variational inference, Markov Chain Monte Carlo samples, or any other method that delivers samples and their likelihood from the unnormalized posterior density. As a physical application, we use $floZ$ to compute the Bayes factor for the presence of the first overtone in the ringdown signal of the gravitational wave data of GW150914, finding good agreement with nested sampling.
