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：嵌套抽样（NS）可计算参数后验分布，并使贝叶斯模型比较在计算上变得可行。其优势在于能够无监督地遍历复杂（可能具有多模态）的后验分布，直至明确定义的终止点。本文对嵌套抽样算法及其变体进行了系统性文献综述。我们重点关注完整的算法，包括对似然约束先验采样、并行化、终止判据及诊断的解决方案。针对两种完整算法，研究了活跃点数、维度与计算成本之间的关系。提出了一种新的NS公式表述，该表述将参数空间探索转化为对树形数据结构的搜索。此前已发表的获取稳健误差估计的方法以及动态调整活跃点数的方案，均被呈现为该公式表述的特例。基于先前的插入排序秩次研究，提出了一种新的在线诊断测试方法。本综述最后对嵌套抽样方法的未来研究方向进行了展望。