Nested sampling statistical errors

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

Submitted on 6 November 2022


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.


Comment: 12 pages + appendices, 3 figures

Subjects: Astrophysics - Instrumentation and Methods for Astrophysics; Physics - Data Analysis, Statistics and Probability; Statistics - Computation