We propose a novel method (floZ), based on normalizing flows, for estimating the Bayesian evidence (and its numerical uncertainty) from a 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. It has wide applicability, e.g., to estimate the evidence from variational inference, Markov-chain Monte Carlo samples, or any other method that delivers samples from the unnormalized posterior density.

翻译：摘要：我们提出了一种基于归一化流的新方法（floZ），用于从非归一化后验分布的样本集中估计贝叶斯证据（及其数值不确定性）。我们在至多15维参数空间的解析已知证据分布上验证了该方法，并与两种最先进的证据估计技术进行了比较：嵌套抽样（以计算证据为主要目标）和一种从后验样本产生证据估计的k近邻技术。在目标后验的代表性样本可获取的前提下，我们的方法对具有尖锐特征的后验分布更加鲁棒，尤其是在高维空间中。该方法具有广泛的适用性，例如可用于变分推断、马尔可夫链蒙特卡洛样本或其他任何能够从非归一化后验密度中生成样本的方法的证据估计。