幻影条件嵌套采样
Phantom-Conditioned Nested Sampling
- California Institute of Technology（加州理工学院）
- Leiden University（莱顿大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文提出幻影条件嵌套采样，利用被丢弃的中间状态改进证据估计，并引入两种动态分配方案，分别减少似然评估次数和增大有效样本量。
中文摘要 AI 辅助
嵌套采样通过将先验体积分配给有序的似然轮廓序列来估计证据。在高维问题中使用的马尔可夫链约束先验采样器，在产生下一个经典样本之前会生成许多中间状态。这些中间状态被丢弃，因为它们的相关性使得在不改变其顺序统计规律的情况下无法将它们插入有序的嵌套采样序列中。本文提出了一种利用这些中间状态来改进证据估计的新方法，通过以贝叶斯方式表述嵌套采样，并将幻影样本作为蒙特卡洛观测进行条件化。随后，我们介绍了开源软件包JAXNS v3及其实现选择。我们在一组问题上验证了该方法，并通过消融实验确定了其局限性。在我们的实验中，当问题结构得到良好解析时，对所有保留的幻影样本进行条件化可使对数证据均方根误差至少降低30%，且在更高维度下改进更大。对于结构未解析的测试问题，完全幻影条件化对证据精度没有产生可检测的改进或恶化。幻影条件化会产生过于自信的证据不确定性。我们还引入了两种动态嵌套采样分配方案。证据改进分配相对于均匀分配，在达到相当证据精度所需的似然评估次数上大约减半。后验改进分配以额外17.5%的似然评估为代价，使经典后验的Kish有效样本量翻倍。
英文摘要
Nested sampling estimates the evidence by assigning prior volumes to an ordered sequence of likelihood contours. Markov chain constrained-prior samplers, which are used in high-dimensional problems, generate many intermediate states before producing the next classic sample. These intermediate states are discarded because their correlation prevents them from being inserted into the ordered NS sequence without changing its order-statistic law. This paper introduces a novel method of using them to improve evidence estimation, by formulating NS in a Bayesian way and conditioning on phantom samples as Monte Carlo observations. We then present the open-source software package, JAXNS v3, and its implementation choices. We validate the approach on a set of problems, and identify its limitations via ablation. In our experiments, when problem structure is well resolved, conditioning on all retained phantom samples reduces log-evidence RMSE by at least $30\%$, with larger improvements at higher dimensionality. For the tested problems with unresolved structure, full phantom conditioning produces no detectable improvement or deterioration in evidence accuracy. Phantom conditioning produces overconfident evidence uncertainties. We also introduce two dynamic nested sampling allocation schemes. Evidence-improving allocation approximately halves the number of likelihood evaluations required to achieve comparable evidence accuracy relative to uniform allocation. Posterior-improving allocation doubles the classic posterior's Kish effective sample size for $17.5\%$ additional likelihood evaluations.
