Nested Sampling Methods. (arXiv:2101.09675v2 [stat.CO] UPDATED)
<a href="http://arxiv.org/find/stat/1/au:+Buchner_J/0/1/0/all/0/1">Johannes Buchner</a>
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. 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 on-line diagnostic test is presented
based on previous insertion rank order work. The survey of nested sampling
methods concludes with outlooks for future research.
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. 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 on-line diagnostic test is presented
based on previous insertion rank order work. The survey of nested sampling
methods concludes with outlooks for future research.
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