Bayesian inference with nested sampling requires a likelihood-restricted prior sampling method, which draws samples from the prior distribution that exceed a likelihood threshold. For high-dimensional problems, Markov Chain Monte Carlo derivatives have been proposed. We numerically study ten algorithms based on slice sampling, hit-and-run and differential evolution algorithms in ellipsoidal, non-ellipsoidal and non-convex problems from 2 to 100 dimensions. Mixing capabilities are evaluated with the nested sampling shrinkage test. This makes our results valid independent of how heavy-tailed the posteriors are. Given the same number of steps, slice sampling is outperformed by hit-and-run and whitened slice sampling, while whitened hit-and-run does not provide as good results. Proposing along differential vectors of live point pairs also leads to the highest efficiencies, and appears promising for multi-modal problems. The tested proposals are implemented in the UltraNest nested sampling package, enabling efficient low and high-dimensional inference of a large class of practical inference problems relevant to astronomy, cosmology, particle physics and astronomy.

翻译：贝叶斯推断中的嵌套采样需要一种似然约束的先验采样方法，该方法从先验分布中抽取超过似然阈值的样本。针对高维问题，已有研究提出基于马尔可夫链蒙特卡洛的改进方法。我们对基于切片采样、跑停采样和差分进化算法的十种算法进行了数值研究，测试场景涵盖2至100维的椭球形、非椭球形及非凸问题。通过嵌套采样收缩测试评估混合能力，使得我们的结果有效性不受后验分布重尾特性的影响。在相同步数条件下，切片采样的表现逊于跑停采样与白化切片采样，而白化跑停采样并未取得同样优异的结果。基于活跃点对差分向量进行提案生成的方法效率最高，且在多模态问题中展现出潜力。所测试的提案方法已在UltraNest嵌套采样工具包中实现，可为天文学、宇宙学、粒子物理学等领域中大量实用推断问题提供高效的低维与高维推理能力。