Open Access
2023 Nested sampling methods
Johannes Buchner
Author Affiliations +
Statist. Surv. 17: 169-215 (2023). DOI: 10.1214/23-SS144


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.

Funding Statement

JB acknowledges support from the CONICYT-Chile grants Basal-CATA PFB-06/2007, FONDECYT Postdoctorados 3160439 and the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics, MAS. This research was supported by the DFG cluster of excellence “Origin and Structure of the Universe”.


I thank the two referees, one of whom was Brendon Brewer, the associate editor and the editor for their constructive comments which improved the paper. I am very thankful to Josh Speagle for feedback and insightful conversations. I am thankful to John Veitch, Matthew Griffiths, David Wales for comments on the manuscript, and Michael Betancourt for insightful conversations.


Download Citation

Johannes Buchner. "Nested sampling methods." Statist. Surv. 17 169 - 215, 2023.


Received: 1 January 2021; Published: 2023
First available in Project Euclid: 26 June 2023

MathSciNet: MR4607531
zbMATH: 07725189
Digital Object Identifier: 10.1214/23-SS144

Vol.17 • 2023
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