English

Nested Sampling Methods

Computation 2023-07-11 v4 Instrumentation and Methods for Astrophysics

Abstract

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.

Keywords

Cite

@article{arxiv.2101.09675,
  title  = {Nested Sampling Methods},
  author = {Johannes Buchner},
  journal= {arXiv preprint arXiv:2101.09675},
  year   = {2023}
}

Comments

Published in Statistics Surveys. The open-source UltraNest package and astrostatistics tutorials can be found at https://johannesbuchner.github.io/UltraNest/