Nested sampling statistical errors

Andrew Fowlie*, Qiao Li, Huifang Lv, Yecheng Sun, Jia Zhang, Le Zheng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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. While 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.

Original languageEnglish
Pages (from-to)4100-4108
Number of pages9
JournalMonthly Notices of the Royal Astronomical Society
Issue number3
Publication statusPublished - 1 May 2023


  • methods: data analysis
  • methods: statistical


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