Nested sampling (NS) computes parameter posterior distributions and makes Bayesian model comparison computationally feasible. Its strengths are the unsupervised navigation of complex, potentially multi-modal posteriors until a well-defined termination point. A systematic literature review of nested sampling algorithms and variants is presented. We focus on complete algorithms, including solutions to likelihood-restricted prior sampling, parallelisation, termination and diagnostics. The relation between number of live points, dimensionality and computational cost is studied for two complete algorithms. A new formulation of NS is presented, which casts the parameter space exploration as a search on a tree data structure. Previously published ways of obtaining robust error estimates and dynamic variations of the number of live points are presented as special cases of this formulation. A new online diagnostic test is presented based on previous insertion rank order work. The survey of nested sampling methods concludes with outlooks for future research.

翻译：嵌套采样（Nested Sampling, NS）可计算参数后验分布，并使得贝叶斯模型比较在计算上变得可行。其优势在于无需监督即可导航复杂（可能为多峰）后验分布，直至明确定义的终止点。本文对嵌套采样算法及其变体进行了系统性文献综述。我们聚焦完整算法，包括受似然约束的先验采样方案、并行化、终止条件及诊断方法。针对两种完整算法，研究了活动点数、维度与计算成本之间的关系。提出了一种新的NS表述形式，将参数空间探索转化为树数据结构上的搜索。此前发表的获取稳健误差估计及动态调整活动点数量的方法，可作为该形式化的特例。基于先前的插入秩次研究工作，提出了一种新型在线诊断测试。对嵌套采样方法的综述以对未来研究方向的展望作结。