Nested sampling for physical scientists

Abstract

We review Skilling's nested sampling (NS) algorithm for Bayesian inference and more broadly multi-dimensional integration. After recapitulating the principles of NS, we survey developments in implementing efficient NS algorithms in practice in high-dimensions, including methods for sampling from the so-called constrained prior. We outline the ways in which NS may be applied and describe the application of NS in three scientific fields in which the algorithm has proved to be useful: cosmology, gravitational-wave astronomy, and materials science. We close by making recommendations for best practice when using NS and by summarizing potential limitations and optimizations of NS.

20 pages + supplementary information, 5 figures. preprint version; published version at https://www.nature.com/articles/s43586-022-00121-x

References in corpus (23)

• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Advanced LIGO
• Bayes in the sky: Bayesian inference and model selection in cosmology
• Robust parameter estimation for compact binaries with ground-based gravitational-wave observations using the LALInference software library
• Supernova Constraints and Systematic Uncertainties from the First 3 Years of the Supernova Legacy Survey
• PolyChord: nested sampling for cosmology
• A statistical test for Nested Sampling algorithms
• The BayesWave analysis pipeline in the era of gravitational wave observations
• Extraction of Gravitational Waves in Numerical Relativity
• Efficient Bayesian inference for multimodal problems in cosmology
• A Bayesian model selection analysis of WMAP3
• anesthetic: nested sampling visualisation
• Helios-r2 -- A new Bayesian, open-source retrieval model for brown dwarfs and exoplanet atmospheres
• Inferring the core-collapse supernova explosion mechanism with gravitational waves
• Hunting Down the Best Model of Inflation with Bayesian Evidence
• Global fits of the dark matter-nucleon effective interactions
• A Bayesian approach to the follow-up of candidate gravitational wave signals
• Fast Bayesian Inference for Exoplanet Discovery in Radial Velocity Data
• Constant-pressure nested sampling with atomistic dynamics
• Constraining the dark energy equation of state using Bayes theorem and the Kullback-Leibler divergence
• The HARPS search for southern extra-solar planets XLV. Two Neptune mass planets orbiting HD 13808: a study of stellar activity modelling's impact on planet detection
• Nested sampling cross-checks using order statistics
• A Thesaurus for Common Priors in Gravitational-Wave Astronomy