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We review Skilling's nested sampling (NS) algorithm for Bayesian inference and more broadly multi-dimensional integration.
Quantifying tensions in cosmological parameters: Interpreting the DES evidence ratio
Handley, W. & Lemos, P · 1902
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Neutrino puzzle: Anomalies, interactions, and cosmological tensions
Kreisch, C. D., Cyr-Racine, F.-Y. & Doré, O · 1902
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Searches for Gravitational Waves from Known Pulsars at Two Harmonics in 2015-2017 LIGO Data
Abbott, B. P. et al · 1902
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DYNESTY: a dynamic nested sampling package for estimating Bayesian posteriors and evidences
Speagle, J. S · 1904
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anesthetic: nested sampling visualisation
Handley, W · 1905
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KiDS+VIKING-450 and DES-Y1 combined: Cosmology with cosmic shear
Joudaki, S. et al · 1906
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Machine-learned interatomic potentials for alloys and alloy phase diagrams
Rosenbrock, C. W. et al · 1906
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New test of modulated electron capture decay of hydrogen-like 142
Ozturk, F. C. et al · 1907
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Gravitational waves from neutron star mergers and their relation to the nuclear equation of state
Baiotti, L · 1907
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Curvature tension: evidence for a closed universe
Handley, W · 1908
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Bayesian inflationary reconstructions from Planck 2018 data
Handley, W. J., Lasenby, A. N., Peiris, H. V. & Hobson, M. P · 1908
Earlier work this paper cites.
Abbott, B. P. et al · 1908
Earlier work this paper cites.
Bayesian automated posterior repartitioning for nested sampling
Chen, X., Feroz, F. & Hobson, M · 1908
Earlier work this paper cites.
Massively parallel Bayesian inference for transient gravitational-wave astronomy
Smith, R. J. E., Ashton, G., Vajpeyi, A. & Talbot, C · 1909
Earlier work this paper cites.
GetDist: a Python package for analysing Monte Carlo samples
Lewis, A · 1910
Earlier work this paper cites.
Helios-r2: A New Bayesian, Open-source Retrieval Model for Brown Dwarfs and Exoplanet Atmospheres
Kitzmann, D. et al · 1910
Earlier work this paper cites.
Statistical mechanics of fluid mixtures
Kirkwood, J. G · 1935
Earlier work this paper cites.
A mathematical theory of communication
Shannon, C. E · 1948
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Equations of state calculations by fast computing machines
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. & Teller, E · 1953
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Curve and periodogram smoothing
Whittle, P · 1957
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An Automatic Method for Finding the Greatest or Least Value of a Function
Rosenbrock, H. H · 1960
Earlier work this paper cites.
Adaptive Control Processes: A Guided Tour
Bellman, R · 1961
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Machine calculation of thermodynamic properties of a simple fluid at supercritical temperatures
McDonald, I. R. & Singer, K · 1967
Earlier work this paper cites.
Prior probabilities
Jaynes, E. T · 1968
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Monte Carlo Sampling Methods Using Markov Chains and Their Applications
Hastings, W. K · 1970
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Bayesian estimates of equation system parameters: An application of integration by Monte Carlo
Kloek, T. & van Dijk, H. K · 1978
Earlier work this paper cites.
A New Approach to Numerical Integration
Burrows, B. L · 1980
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Inflationary universe: A possible solution to the horizon and flatness problems
Guth, A. H · 1981
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The Well-Calibrated Bayesian
Dawid, A. P · 1982
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Microcanonical Monte Carlo simulation
Creutz, M · 1983
Earlier work this paper cites.
Optimization by simulated annealing
Kirkpatrick, S., Gelatt, C. D. G. & Vecchi, M. P · 1983
Earlier work this paper cites.
Efficient monte carlo procedures for generating points uniformly distributed over bounded regions
Smith, R. L · 1984
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Accurate approximations for posterior moments and marginal densities
Tierney, L. & Kadane, J. B · 1986
Earlier work this paper cites.
Monte Carlo-minimization approach to the multiple-minima problem in protein folding
Li, Z. & Scheraga, H. A · 1987
Earlier work this paper cites.
Hybrid Monte Carlo
Duane, S., Kennedy, A., Pendleton, B. J. & Roweth, D · 1987
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Approximate Bayesian inference with the weighted likelihood bootstrap
Newton, M. A. & Raftery, A. E · 1994
Earlier work this paper cites.
Formalizing the slow-roll approximation in inflation
Liddle, A. R., Parsons, P. & Barrow, J. D · 1994
Earlier work this paper cites.
Bayes factors
Kass, R. E. & Raftery, A. E · 1995
Earlier work this paper cites.
Marginal likelihood from the Gibbs output
Chib, S · 1995
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The topology of multidimensional potential energy surfaces: Theory and application to peptide structure and kinetics
Becker, O. M. & Karplus, M · 1997
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Global optimization by basin-hopping and the lowest energy structures of lennard-jones clusters containing up to 110 atoms
Wales, D. J. & Doye, J. P. K · 1997
Earlier work this paper cites.
Simulating normalizing constants: from importance sampling to bridge sampling to path sampling
Gelman, A. & Meng, X.-L · 1998
Earlier work this paper cites.
Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
Riess, A. G. et al · 1998
Earlier work this paper cites.
A Supersymmetry primer
Martin, S. P · 1998
Earlier work this paper cites.
Archetypal energy landscapes
Wales, D. J., Miller, M. A. & Walsh, T. R · 1998
Earlier work this paper cites.
Measurements of Ω \Omega and λ \lambda from 42 High-Redshift Supernovae
Perlmutter, S. et al · 1999
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Global optimization of clusters, crystals and biomolecules
Wales, D. J. & Scheraga, H. A · 1999
Earlier work this paper cites.
Thermodynamics of supercooled liquids in the inherent-structure formalism: a case study
Sciortino, F., Kob, W. & Tartaglia, P · 2000
Earlier work this paper cites.
Estimation of small failure probabilities in high dimensions by subset simulation
Au, S.-K. & Beck, J. L · 2001
Earlier work this paper cites.
Efficient, multiple-range random walk algorithm to calculate the density of states
Wang, F. & Landau, D. P · 2001
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Cosmological constraints from the X-ray gas mass fraction in relaxed lensing clusters observed with chandra
Allen, S. W., Schmidt, R. W. & Fabian, A. C · 2002
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Free energy disconnectivity graphs: Application to peptide models
Krivov, S. V. & Karplus, M · 2002
Earlier work this paper cites.
Cosmological parameters from CMB and other data: A Monte Carlo approach
Lewis, A. & Bridle, S · 2002
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Bayesian Reasoning In Data Analysis: A Critical Introduction (World Scientific Publishing Company, 2003)
D’Agostini, G · 2003
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First-year wilkinson microwave anisotropy probe ( WMAP ) observations: Determination of cosmological parameters
Spergel, D. N. et al · 2003
Earlier work this paper cites.
Energy Landscapes (Cambridge University Press, Cambridge, 2003)
Wales, D. J · 2003
Earlier work this paper cites.
Free energy landscapes of model peptides and proteins
Evans, D. A. & Wales, D. J · 2003
Earlier work this paper cites.
Information Theory, Inference and Learning Algorithms (Cambridge University Press, 2003)
MacKay, D. J. C · 2003
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Nested Sampling
Skilling, J · 2004
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Computing Bayes: Bayesian Computation from 1763 to the 21st Century
Martin, G. M., Frazier, D. T. & Robert, C. P · 2004
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Bayesian Logical Data Analysis for the Physical Sciences (Cambridge University Press, 2005)
Gregory, P · 2005
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Marginal likelihood computation for model selection and hypothesis testing: an extensive review
Llorente, F., Martino, L., Delgado, D. & Lopez-Santiago, J · 2005
Earlier work this paper cites.
The energy landscape as a unifying theme in molecular science
Wales, D. J · 2005
Earlier work this paper cites.
Nested sampling for Potts models
Murray, I., MacKay, D. J. C., Ghahramani, Z. & Skilling, J · 2005
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Nested Sampling And Likelihood Plateaus
Schittenhelm, D. & Wacker, P · 2005
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Nested sampling for general Bayesian computation
Skilling, J · 2006
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Data Analysis: A Bayesian Tutorial (Oxford University Press, 2006). Sivia & Skilling’s popular textbook includes a chapter on NS
Sivia, D. & Skilling, J · 2006
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A Nested Sampling Algorithm for Cosmological Model Selection
Mukherjee, P., Parkinson, D. & Liddle, A. R · 2006
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Bayesian model selection analysis of WMAP3
Parkinson, D., Mukherjee, P. & Liddle, A. R · 2006
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A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: easy Bayesian computing for real parameter spaces
Ter Braak, C. J. F · 2006
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Nested sampling cross-checks using order statistics
Fowlie, A., Handley, W. & Su, L · 2006
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Romero-Shaw, I. M. et al · 2006
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A Markov chain Monte Carlo analysis of the CMSSM
de Austri, R. R., Trotta, R. & Roszkowski, L · 2006
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Potential energy and free energy landscapes
Wales, D. J. & Bogdan, T. V · 2006
Earlier work this paper cites.
Validation of software for Bayesian models using posterior quantiles
Cook, S. R., Gelman, A. & Rubin, D. B · 2006
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Discussion of nested sampling for Bayesian computations by John Skilling
Evans, M · 2007
Earlier work this paper cites.
Efficient Bayesian inference for multimodal problems in cosmology
Shaw, J. R., Bridges, M. & Hobson, M. P · 2007
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KiDS-1000 cosmology: Cosmic shear constraints and comparison between two point statistics
Asgari, M. et al · 2007
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The Post-Newtonian Approximation for Relativistic Compact Binaries
Futamase, T. & Itoh, Y · 2007
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Advances in Markov chain Monte Carlo methods
Murray, I · 2007
Earlier work this paper cites.
Matplotlib: A 2d graphics environment
Hunter, J. D · 2007
Cited alongside, same era.
Bayes in the sky: Bayesian inference and model selection in cosmology
Trotta, R · 2008
Cited alongside, same era.
Feroz, F. & Hobson, M. P · 2008
Cited alongside, same era.
The Impact of priors and observables on parameter inferences in the Constrained MSSM
Trotta, R., Feroz, F., Hobson, M. P., Roszkowski, L. & de Austri, R. R · 2008
Cited alongside, same era.
A Bayesian approach to the follow-up of candidate gravitational wave signals
Veitch, J. & Vecchio, A · 2008
A statistical test for Nested Sampling algorithms
Buchner, J · 2016
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Determining the pressure-temperature phase diagrams of materials
Baldock, R. J. N., Pártay, L. B., Bartók, A. P., Payne, M. C. & Csányi, G · 2016
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Superplot: a graphical interface for plotting and analysing MultiNest output
Fowlie, A. & Bardsley, M. H · 2016
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corner.py: Scatterplot matrices in python
Foreman-Mackey, D · 2016
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pygtc: beautiful parameter covariance plots (aka. giant triangle confusograms)
Bocquet, S. & Carter, F. W · 2016
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Cited alongside, same era.
Probability and Information: An Integrated Approach (Cambridge University Press, 2008)
Applebaum, D · 2008
Cited alongside, same era.
Nested Sampling’s Convergence
Skilling, J · 2009
Cited alongside, same era.
Computational methods for Bayesian model choice
Robert, C. P. & Wraith, D · 2009
Cited alongside, same era.
MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics
Feroz, F., Hobson, M. P. & Bridges, M · 2009
Cited alongside, same era.
Bayesian modelling of clusters of galaxies from multifrequency-pointed Sunyaev-Zel’dovich observations
Feroz, F., Hobson, M. P., Zwart, J. T. L., Saunders, R. D. E. & Grainge, K. J. B · 2009
Cited alongside, same era.
CosmoBit: a GAMBIT module for computing cosmological observables and likelihoods
Renk, J. J. et al · 2009
Cited alongside, same era.
Stöcker, P. et al · 2009
Cited alongside, same era.
Equidistribution testing with Bayes factors and the ECT
Stokes, B., Tuyl, F. & Hudson, I · 2016
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Measurement of the charged pion mass using X-ray spectroscopy of exotic atoms
Trassinelli, M. et al · 2016
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Planck 2015 results. XX. Constraints on inflation
Planck Collaboration · 2016
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Testable Baryogenesis in Seesaw Models
Hernández, P., Kekic, M., López-Pavón, J., Racker, J. & Salvado, J · 2016
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Observation of Gravitational Waves from a Binary Black Hole Merger
Abbott, B. P. et al · 2016
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Inferring the core-collapse supernova explosion mechanism with gravitational waves
Powell, J., Gossan, S. E., Logue, J. & Heng, I. S · 2016
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Extraction of gravitational waves in numerical relativity
Bishop, N. T. & Rezzolla, L · 2016
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GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
Abbott, B. P. et al · 2016
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The FAIR guiding principles for scientific data management and stewardship
Wilkinson, M. D. et al · 2016
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Practical Bayesian Inference: A Primer for Physical Scientists (Cambridge University Press, 2017)
Bailer-Jones, C. A. L · 2017
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Constant-pressure nested sampling with atomistic dynamics
Baldock, R. J. N., Bernstein, N., Salerno, K. M., Pártay, L. B. & Csányi, G · 2017
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New prior sampling methods for nested sampling — Development and testing
Stokes, B., Tuyl, F. & Hudson, I · 2017
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Combined-chain nested sampling for efficient Bayesian model comparison
Henderson, R. W., Goggans, P. M. & Cao, L · 2017
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Room acoustic modal analysis using Bayesian inference
Beaton, D. & Xiang, N · 2017
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Bayesian data analysis tools for atomic physics
Trassinelli, M · 2017
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Lavie, B. et al · 2017
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Dynamical dark energy in light of the latest observations
Zhao, G.-B. et al · 2017
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Hee, S., Vázquez, J. A., Handley, W. J., Hobson, M. P. & Lasenby, A. N · 2017
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Comparison of statistical sampling methods with scannerbit, the GAMBIT scanning module
Martinez, G. et al · 2017
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A nested sampling code for targeted searches for continuous gravitational waves from pulsars
Pitkin, M., Isi, M., Veitch, J. & Woan, G · 2017
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Information-theoretic approach to the gravitational-wave burst detection problem
Lynch, R., Vitale, S., Essick, R., Katsavounidis, E. & Robinet, F · 2017
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Data analysis recipes: Using Markov Chain Monte Carlo
Hogg, D. W. & Foreman-Mackey, D · 2018
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Unbiased and consistent nested sampling via sequential Monte Carlo
Salomone, R., South, L. F., Drovandi, C. C. & Kroese, D. P · 2018
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Dynamic nested sampling: an improved algorithm for parameter estimation and evidence calculation
Higson, E., Handley, W., Hobson, M. & Lasenby, A · 2018
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dyPolyChord: dynamic nested sampling with PolyChord
Higson, E · 2018
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nestcheck: error analysis, diagnostic tests and plots for nested sampling calculations
Higson, E · 2018
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New prior sampling methods and equidistribution testing for nested sampling
Stokes, B. J · 2018
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Line shape analysis of the K β \beta transition in muonic hydrogen
Covita, D. S. et al · 2018
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Machado, J. et al · 2018
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On the Feasibility of Intense Radial Velocity Surveys for Earth-Twin Discoveries
Hall, R. D., Thompson, S. J., Handley, W. & Queloz, D · 2018
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Dark Energy Survey year 1 results: Cosmological constraints from galaxy clustering and weak lensing
DES Collaboration · 2018
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Optimal search for an astrophysical gravitational-wave background
Smith, R. & Thrane, E · 2018
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Direct Computation of the Quantum Partition Function by Path-Integral Nested Sampling
Szekeres, B., Pártay, L. B. & Mátyus, E · 2018
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Nested transition path sampling
Bolhuis, P. G. & Csányi, G · 2018
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Nested sampling, statistical physics and the Potts model
Pfeifenberger, M. J., Rumetshofer, M. & von der Linden, W · 2018
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On the performance of interatomic potential models of iron: comparison of the phase diagrams
Pártay, L. B · 2018
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A Conceptual Introduction to Hamiltonian Monte Carlo
Betancourt, M · 2018
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Validating Bayesian Inference Algorithms with Simulation-Based Calibration
Talts, S., Betancourt, M., Simpson, D., Vehtari, A. & Gelman, A · 2018
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Sampling errors in nested sampling parameter estimation
Higson, E., Handley, W., Hobson, M. & Lasenby, A · 2018
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Rotskoff, G. M. & Vanden-Eijnden, E · 2019
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Collaborative Nested Sampling: Big Data versus Complex Physical Models
Buchner, J · 2019
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Nested basin-sampling
Griffiths, M. & Wales, D. J · 2019
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NESTCHECK: diagnostic tests for nested sampling calculations
Higson, E., Handley, W., Hobson, M. & Lasenby, A · 2019
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Importance Nested Sampling and the MultiNest Algorithm
Feroz, F., Hobson, M. P., Cameron, E. & Pettitt, A. N · 2019
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Model selection and parameter inference in phylogenetics using nested sampling
Russel, P. M., Brewer, B. J., Klaere, S. & Bouckaert, R. R · 2019
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Assessing the surface oxidation state of free-standing gold nanoparticles produced by laser ablation
De Anda Villa, M. et al · 2019
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Constraining the kinetically dominated universe
Hergt, L. T., Handley, W. J., Hobson, M. P. & Lasenby, A. N · 2019
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Bayesian sparse reconstruction: a brute-force approach to astronomical imaging and machine learning
Higson, E., Handley, W., Hobson, M. & Lasenby, A · 2019
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Thrane, E. & Talbot, C · 2019
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Neutron star parameter estimation from a NICER perspective
Riley, T. E · 2019
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Improving the efficiency and robustness of nested sampling using posterior repartitioning
Chen, X., Hobson, M., Das, S. & Gelderblom, P · 2019
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Constrained space MCMC methods for nested sampling Bayesian computations
Olander, J · 2020
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Likelihood-free nested sampling for parameter inference of biochemical reaction networks
Mikelson, J. & Khammash, M · 2020
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Detrending the waveforms of steady-state vowels
Van Soom, M. & de Boer, B · 2020
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Pressure–Temperature Phase Diagram of Lithium, Predicted by Embedded Atom Model Potentials
Dorrell, J. & Pártay, L. B · 2020
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Array programming with NumPy
Harris, C. R. et al · 2020
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SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python
Virtanen, P. et al · 2020
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Bayesian statistics and modelling
van de Schoot, R. et al · 2021
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NEO: Non Equilibrium Sampling on the Orbits of a Deterministic Transform
Thin, A. et al · 2021
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Buchner, J · 2021
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nessai: Nested Sampling with Artificial Intelligence, DOI: 10.5281/zenodo.4550693 (2021)
Williams, M. J · 2021
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Nested sampling with normalizing flows for gravitational-wave inference
Williams, M. J., Veitch, J. & Messenger, C · 2021
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UltraNest - a robust, general purpose Bayesian inference engine
Buchner, J · 2021
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Ahrer, E. et al · 2021
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Constraining quantum initial conditions before inflation
Gessey-Jones, T. & Handley, W. J · 2021
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A comparison of optimisation algorithms for high-dimensional particle and astrophysics applications
Balázs, C. et al · 2021
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Abbott, R. et al · 2021
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A Thesaurus for Common Priors in Gravitational-Wave Astronomy
Callister, T. A · 2021
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Insight into liquid polymorphism from the complex phase behavior of a simple model
Bartók, A. P., Hantal, G. & Pártay, L. B · 2021
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Gaussian process regression for materials and molecules
Deringer, V. L. et al · 2021
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Nested sampling for materials
Pártay, L. B., Csányi, G. & Bernstein, N · 2021
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Hergt, L. T., Handley, W. J., Hobson, M. P. & Lasenby, A. N · 2021
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Nested sampling with any prior you like
Alsing, J. & Handley, W · 2021
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Nested Sampling for Frequentist Computation: Fast Estimation of Small p-Values
Fowlie, A., Hoof, S. & Handley, W · 2022
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