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.
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.
"Nested sampling methods." Statist. Surv. 17 169 - 215, 2023. https://doi.org/10.1214/23-SS144