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.

我们提出了一种基于归一化流的新方法 (floZ)，用于从一组从非归一化后验分布中抽取的样本中估计贝叶斯证据 (及其数值不确定性)。通过在已知解析证据的分布上进行验证，最多可达到 15 个参数空间维度，并与两种先进的技术进行比较，这两种技术均用于估计证据：嵌套采样 (将证据作为其主要目标进行计算) 和通过后验样本产生证据估计的 k 最近邻技术。如果有来自目标后验的代表样本可用，我们的方法对于具有尖锐特征的后验分布具有更好的鲁棒性，特别是在较高维度上。它具有广泛的适用性，例如用于估计变分推断、Markov 链蒙特卡洛样本或从非归一化后验密度中提供样本的任何其他方法。