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Nested sampling methods
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AI
DOI：10.1214/23-SS144.png)
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Abstract
En 中文
Nested sampling (NS) computes parameter posterior distribu-tions 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 liter-ature 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:
MONTE-CARLO
MARGINAL LIKELIHOOD
EFFICIENT
COMPUTATION