Nested sampling (NS) is a popular algorithm for Bayesian computation. We investigate statistical errors in NS both analytically and numerically. We show two analytic results. First, we show that the leading terms in Skilling's expression using information theory match the leading terms in Keeton's expression from an analysis of moments. This approximate agreement was previously only known numerically and was somewhat mysterious. Second, we show that the uncertainty in single NS runs approximately equals the standard deviation in repeated NS runs. Whilst intuitive, this was previously taken for granted. We close by investigating our results and their assumptions in several numerical examples, including cases in which NS uncertainties increase without bound.

翻译：括号抽样(NS)是贝叶斯计算中流行的算法。 我们从分析和数字两方面对NS的统计错误进行调查。 我们展示了两个分析结果。 首先, 我们显示, 使用信息理论的技巧表达方式中的主要术语与基顿的表达方式中从对时间的分析中得出的主要术语相匹配。 这种近似一致在数字上是已知的, 有点神秘。 其次, 我们显示, 单NS 的不确定性与重复NS 运行时的标准偏差大致相等。 虽然直观地说, 这一点过去是理所当然的。 我们最后通过调查我们的结果及其假设, 在几个数字例子中, 包括无约束地增加NS 不确定性的案例 。