Nested sampling statistical errors

Nested sampling statistical errors

ABSTRACT 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 K...

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Veröffentlicht in:Monthly notices of the Royal Astronomical Society 2023-05, Vol.521 (3), p.4100-4108
Hauptverfasser: Fowlie, Andrew, Li, Qiao, Lv, Huifang, Sun, Yecheng, Zhang, Jia, Zheng, Le
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creator Fowlie, Andrew
Li, Qiao
Lv, Huifang
Sun, Yecheng
Zhang, Jia
Zheng, Le
description ABSTRACT 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.
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