Nested Sampling Methods

TL;DR

This paper provides a comprehensive review of nested sampling algorithms, introduces a new formulation using tree structures, and discusses diagnostics and future research directions for Bayesian computation.

Contribution

It offers a systematic review, introduces a novel tree-based formulation of nested sampling, and presents new diagnostics and error estimation methods.

Findings

Relation between live points, dimensionality, and cost analyzed

New tree-based formulation of nested sampling introduced

A novel online diagnostic test for nested sampling proposed

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.