Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis
Farhan Feroz,Michael P. Hobson +1 more
TLDR
Three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies in very high dimensions are presented, leading to a further substantial improvement in sampling efficiency and robustness and an even more efficient technique for estimating the uncertainty on the evaluated evidence.Abstract:
In performing a Bayesian analysis of astronomical data, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multimodal or exhibit pronounced (curving) degeneracies, which can cause problems for traditional MCMC sampling methods. Second, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally expensive. The nested sampling method introduced by Skilling (2004), has greatly reduced the computational expense of calculating evidences and also produces posterior inferences as a by-product. This method has been applied successfully in cosmological applications by Mukherjee et al. (2006), but their implementation was efficient only for unimodal distributions without pronounced degeneracies. Shaw et al. (2007), recently introduced a clustered nested sampling method which is significantly more efficient in sampling from multimodal posteriors and also determines the expectation and variance of the final evidence from a single run of the algorithm, hence providing a further increase in efficiency. In this paper, we build on the work of Shaw et al. and present three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies; we also present an even more efficient technique for estimating the uncertainty on the evaluated evidence. These methods lead to a further substantial improvement in sampling efficiency and robustness, and are applied to toy problems to demonstrate the accuracy and economy of the evidence calculation and parameter estimation. Finally, we discuss the use of these methods in performing Bayesian object detection in astronomical datasets.read more
Citations
More filters
Journal ArticleDOI
Planck 2015 results. XX. Constraints on inflation
Peter A. R. Ade,Nabila Aghanim,Monique Arnaud,Frederico Arroja,M. Ashdown,J. Aumont,Carlo Baccigalupi,Mario Ballardini,A. J. Banday,R. B. Barreiro,Nicola Bartolo,E. Battaner,K. Benabed,Alain Benoit,A. Benoit-Lévy,J.-P. Bernard,Marco Bersanelli,P. Bielewicz,J. J. Bock,Anna Bonaldi,Laura Bonavera,J. R. Bond,Julian Borrill,François R. Bouchet,F. Boulanger,M. Bucher,Carlo Burigana,R. C. Butler,Erminia Calabrese,Jean-François Cardoso,A. Catalano,Anthony Challinor,A. Chamballu,R.-R. Chary,H. C. Chiang,P. R. Christensen,Sarah E. Church,David L. Clements,S. Colombi,L. P. L. Colombo,C. Combet,D. Contreras,F. Couchot,A. Coulais,B. P. Crill,A. Curto,F. Cuttaia,Luigi Danese,R. D. Davies,R. J. Davis,P. de Bernardis,A. de Rosa,G. de Zotti,Jacques Delabrouille,F.-X. Désert,Jose M. Diego,H. Dole,S. Donzelli,Olivier Doré,Marian Douspis,A. Ducout,X. Dupac,George Efstathiou,F. Elsner,Torsten A. Ensslin,H. K. Eriksen,James R. Fergusson,Fabio Finelli,Olivier Forni,M. Frailis,Aurelien A. Fraisse,E. Franceschi,A. Frejsel,Andrei V. Frolov,S. Galeotta,Silvia Galli,K. Ganga,C. Gauthier,M. Giard,Y. Giraud-Héraud,E. Gjerløw,J. González-Nuevo,Krzysztof M. Gorski,Serge Gratton,A. Gregorio,Alessandro Gruppuso,Jon E. Gudmundsson,Jan Hamann,Will Handley,F. K. Hansen,Duncan Hanson,D. L. Harrison,Sophie Henrot-Versille,C. Hernández-Monteagudo,D. Herranz,S. R. Hildebrandt,E. Hivon,Michael P. Hobson,W. A. Holmes +98 more
TL;DR: In this article, the authors report on the implications for cosmic inflation of the 2018 Release of the Planck CMB anisotropy measurements, which are fully consistent with the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles.
Journal ArticleDOI
MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics
TL;DR: The developments presented here lead to further improvements in sampling efficiency and robustness, as compared to the original algorit hm presented in Feroz & Hobson (2008), which itself significantly outperformed existi ng MCMC techniques in a wide range of astrophysical inference problems.
Journal ArticleDOI
Planck 2013 results. XXII. Constraints on inflation
Peter A. R. Ade,Nabila Aghanim,Monique Arnaud,Frederico Arroja,Frederico Arroja,M. Ashdown,J. Aumont,Carlo Baccigalupi,Mario Ballardini,A. J. Banday,A. J. Banday,R. B. Barreiro,Nicola Bartolo,Nicola Bartolo,E. Battaner,K. Benabed,Alain Benoit,A. Benoit-Lévy,A. Benoit-Lévy,J.-P. Bernard,J.-P. Bernard,Marco Bersanelli,Marco Bersanelli,P. Bielewicz,P. Bielewicz,James J. Bock,Anna Bonaldi,Laura Bonavera,J. R. Bond,Julian Borrill,Julian Borrill,François R. Bouchet,Francois Boulanger,M. Bucher,Carlo Burigana,Carlo Burigana,R. C. Butler,Erminia Calabrese,Jean-François Cardoso,Jean-François Cardoso,Jean-François Cardoso,A. Catalano,A. Catalano,Anthony Challinor,A. Chamballu,A. Chamballu,A. Chamballu,R.-R. Chary,H. C. Chiang,H. C. Chiang,P. R. Christensen,Sarah E. Church,David L. Clements,S. Colombi,L. P. L. Colombo,L. P. L. Colombo,C. Combet,D. Contreras,F. Couchot,A. Coulais,B. P. Crill,A. Curto,A. Curto,F. Cuttaia,Luigi Danese,R. D. Davies,R. J. Davis,P. de Bernardis,A. de Rosa,G. de Zotti,G. de Zotti,Jacques Delabrouille,F.-X. Désert,Jose M. Diego,H. Dole,H. Dole,S. Donzelli,Olivier Doré,Marian Douspis,A. Ducout,A. Ducout,X. Dupac,George Efstathiou,F. Elsner,F. Elsner,Torsten A. Enßlin,H. K. Eriksen,James R. Fergusson,Fabio Finelli,Olivier Forni,Olivier Forni,M. Frailis,Aurelien A. Fraisse,E. Franceschi,A. Frejsel,Andrei V. Frolov,S. Galeotta,S. Galli,K. Ganga,C. Gauthier,C. Gauthier,M. Giard,M. Giard,Y. Giraud-Héraud,E. Gjerløw,J. González-Nuevo,J. González-Nuevo,Krzysztof M. Gorski,Krzysztof M. Gorski,Serge Gratton,A. Gregorio,A. Gregorio,Alessandro Gruppuso,Jon E. Gudmundsson,Jon E. Gudmundsson,Jon E. Gudmundsson,Jan Hamann,Jan Hamann,Will Handley,F. K. Hansen,Duncan Hanson,Duncan Hanson,Duncan Hanson,D. L. Harrison,Sophie Henrot-Versille,C. Hernández-Monteagudo,D. Herranz,S. R. Hildebrandt,E. Hivon,Michael P. Hobson,W. A. Holmes,Allan Hornstrup,W. Hovest,Zhiqi Huang,Kevin M. Huffenberger,G. Hurier,Andrew H. Jaffe,T. R. Jaffe,T. R. Jaffe,W. C. Jones,Mika Juvela,E. Keihänen,Reijo Keskitalo,J. B. Kim,Theodore Kisner,R. Kneissl,R. Kneissl,J. Knoche,Martin Kunz,Martin Kunz,Martin Kunz,Hannu Kurki-Suonio,Hannu Kurki-Suonio,Guilaine Lagache,Guilaine Lagache,Anne Lähteenmäki,Anne Lähteenmäki,J.-M. Lamarre,Anthony Lasenby,Massimiliano Lattanzi,Charles R. Lawrence,R. Leonardi,Julien Lesgourgues,Julien Lesgourgues,François Levrier,Antony Lewis,Michele Liguori,Michele Liguori,P. B. Lilje,M. Linden-Vørnle,M. López-Caniego,M. López-Caniego,Philip Lubin,Yin-Zhe Ma,Yin-Zhe Ma,J. F. Macías-Pérez,Gianmarco Maggio,Davide Maino,Davide Maino,N. Mandolesi,N. Mandolesi,A. Mangilli,A. Mangilli,Michele Maris,Peter G. Martin,E. Martínez-González,Silvia Masi,Sabino Matarrese,Sabino Matarrese,P. M. McGehee,Peter Meinhold,Alessandro Melchiorri,L. Mendes,A. Mennella,A. Mennella,M. Migliaccio,Subhabrata Mitra,Subhabrata Mitra,M.-A. Miville-Deschênes,M.-A. Miville-Deschênes,D. Molinari,D. Molinari,A. Moneti,L. Montier,L. Montier,Gianluca Morgante,Daniel J. Mortlock,Adam Moss,Moritz Münchmeyer,Dipak Munshi,J. A. Murphy,Pavel Naselsky,Federico Nati,Paolo Natoli,Paolo Natoli,Paolo Natoli,Calvin B. Netterfield,Hans Ulrik Nørgaard-Nielsen,F. Noviello,Dmitry Novikov,I. D. Novikov,I. D. Novikov,Carol Anne Oxborrow,F. Paci,L. Pagano,F. Pajot,Roberta Paladini,S. Pandolfi,Daniela Paoletti,Fabio Pasian,G. Patanchon,T. J. Pearson,Hiranya V. Peiris,O. Perdereau,L. Perotto,Francesca Perrotta,Valeria Pettorino,F. Piacentini,M. Piat,Elena Pierpaoli,Davide Pietrobon,Stéphane Plaszczynski,Etienne Pointecouteau,Etienne Pointecouteau,G. Polenta,G. Polenta,L. Popa,G. W. Pratt,G. Prézeau,Simon Prunet,J.-L. Puget,Jörg P. Rachen,Jörg P. Rachen,William T. Reach,Rafael Rebolo,Rafael Rebolo,M. Reinecke,Mathieu Remazeilles,Mathieu Remazeilles,Mathieu Remazeilles,C. Renault,A. Renzi,I. Ristorcelli,I. Ristorcelli,Graca Rocha,C. Rosset,M. Rossetti,M. Rossetti,G. Roudier,G. Roudier,G. Roudier,Michael Rowan-Robinson,Jose Alberto Rubino-Martin,Jose Alberto Rubino-Martin,Ben Rusholme,M. Sandri,D. Santos,M. Savelainen,M. Savelainen,Giorgio Savini,Douglas Scott,M. D. Seiffert,E. P. S. Shellard,Maresuke Shiraishi,Maresuke Shiraishi,Locke D. Spencer,V. Stolyarov,V. Stolyarov,V. Stolyarov,Radek Stompor,R. V. Sudiwala,R. A. Sunyaev,R. A. Sunyaev,D. Sutton,A.-S. Suur-Uski,A.-S. Suur-Uski,J.-F. Sygnet,J. A. Tauber,Luca Terenzi,Luca Terenzi,L. Toffolatti,L. Toffolatti,L. Toffolatti,M. Tomasi,M. Tomasi,Matthieu Tristram,Tiziana Trombetti,M. Tucci,J. Tuovinen,Luca Valenziano,Jussi Valiviita,Jussi Valiviita,B. Van Tent,P. Vielva,Fabrizio Villa,Lawrence A. Wade,Benjamin D. Wandelt,Benjamin D. Wandelt,Ingunn Kathrine Wehus,Ingunn Kathrine Wehus,Martin White,D. Yvon,Andrea Zacchei,J. P. Zibin,Andrea Zonca +324 more
TL;DR: In this article, the authors present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey.
Journal ArticleDOI
Cosmology and Fundamental Physics with the Euclid Satellite
Luca Amendola,Stephen Appleby,Anastasios Avgoustidis,David Bacon,Tessa Baker,Marco Baldi,Marco Baldi,Marco Baldi,Nicola Bartolo,Nicola Bartolo,Alain Blanchard,Camille Bonvin,Stefano Borgani,Stefano Borgani,Enzo Branchini,Enzo Branchini,Clare Burrage,Stefano Camera,Carmelita Carbone,Carmelita Carbone,Luciano Casarini,Luciano Casarini,Mark Cropper,Claudia de Rham,J. P. Dietrich,Cinzia Di Porto,Ruth Durrer,Anne Ealet,Pedro G. Ferreira,Fabio Finelli,Juan Garcia-Bellido,Tommaso Giannantonio,Luigi Guzzo,Luigi Guzzo,Alan Heavens,Lavinia Heisenberg,Catherine Heymans,Henk Hoekstra,Lukas Hollenstein,Rory Holmes,Zhiqi Hwang,Knud Jahnke,Thomas D. Kitching,Tomi S. Koivisto,Martin Kunz,Giuseppe Vacca,Eric V. Linder,M. March,Valerio Marra,Carlos Martins,Elisabetta Majerotto,Dida Markovic,David J. E. Marsh,Federico Marulli,Federico Marulli,Richard Massey,Yannick Mellier,Francesco Montanari,David F. Mota,Nelson J. Nunes,Will J. Percival,Valeria Pettorino,Valeria Pettorino,Cristiano Porciani,Claudia Quercellini,Justin I. Read,Massimiliano Rinaldi,Domenico Sapone,Ignacy Sawicki,Roberto Scaramella,Constantinos Skordis,Constantinos Skordis,Fergus Simpson,Andy Taylor,Shaun A. Thomas,Roberto Trotta,Licia Verde,Filippo Vernizzi,Adrian Vollmer,Yun Wang,Jochen Weller,T. G. Zlosnik +81 more
TL;DR: Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015-2025 program as discussed by the authors, which will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shift of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky.
Journal ArticleDOI
Bayes in the sky: Bayesian inference and model selection in cosmology
TL;DR: This review is an introduction to Bayesian methods in cosmology and astrophysics and recent results in the field, and presents Bayesian probability theory and its conceptual underpinnings, Bayes' Theorem and the role of priors.
References
More filters
Book
Information Theory, Inference and Learning Algorithms
TL;DR: A fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.
Book
Information theory, inference, and learning algorithms
TL;DR: In this paper, the mathematics underpinning the most dynamic areas of modern science and engineering are discussed and discussed in a fun and exciting textbook on the mathematics underlying the most important areas of science and technology.
Book
Data analysis : a Bayesian tutorial
TL;DR: This tutorial jumps right in to the power ofparameter estimation without dragging you through the basic concepts of parameter estimation.
Journal ArticleDOI
First-Year Wilkinson Microwave Anisotropy Probe (WMAP)* Observations: Foreground Emission
Charles L. Bennett,Robert S. Hill,Gary Hinshaw,M. R. Nolta,N. Odegard,Lyman A. Page,David N. Spergel,Janet L. Weiland,Edward L. Wright,Mark Halpern,N. Jarosik,Alan J. Kogut,Michele Limon,Michele Limon,S. S. Meyer,Gregory S. Tucker,Gregory S. Tucker,Gregory S. Tucker,Edward J. Wollack +18 more
TL;DR: In this article, the authors used a maximum entropy method to construct a model of the Galactic emission components and showed that the model is accurate to less than 1% and individual model components are accurate to a few percent.
Journal ArticleDOI
Information criteria for astrophysical model selection
TL;DR: The Deviance Information Criterion as mentioned in this paper combines ideas from both heritages; it is readily computed from Monte Carlo posterior samples and, unlike the AIC and BIC, allows for parameter degeneracy.
Related Papers (5)
Planck 2015 results. XIII. Cosmological parameters
Peter A. R. Ade,Nabila Aghanim,Monique Arnaud,M. Ashdown,J. Aumont,Carlo Baccigalupi,A. J. Banday,R. B. Barreiro,James G. Bartlett,N. Bartolo,E. Battaner,Richard A. Battye,K. Benabed,Alain Benoit,A. Benoit-Lévy,J.-P. Bernard,Marco Bersanelli,P. Bielewicz,J. J. Bock,Anna Bonaldi,Laura Bonavera,J. R. Bond,Julian Borrill,François R. Bouchet,F. Boulanger,M. Bucher,Carlo Burigana,R. C. Butler,Erminia Calabrese,Jean-François Cardoso,A. Catalano,Anthony Challinor,A. Chamballu,Ranga-Ram Chary,H. C. Chiang,Jens Chluba,P. R. Christensen,Sarah E. Church,David L. Clements,S. Colombi,L. P. L. Colombo,C. Combet,A. Coulais,B. P. Crill,A. Curto,F. Cuttaia,Luigi Danese,R. D. Davies,R. J. Davis,P. de Bernardis,A. de Rosa,G. de Zotti,Jacques Delabrouille,F.-X. Désert,E. Di Valentino,Clive Dickinson,Jose M. Diego,Klaus Dolag,H. Dole,S. Donzelli,Olivier Doré,Marian Douspis,A. Ducout,Jo Dunkley,X. Dupac,George Efstathiou,F. Elsner,Torsten A. Ensslin,H. K. Eriksen,Marzieh Farhang,James R. Fergusson,Fabio Finelli,Olivier Forni,M. Frailis,A. A. Fraisse,E. Franceschi,A. Frejsel,S. Galeotta,S. Galli,K. Ganga,C. Gauthier,Martina Gerbino,Tuhin Ghosh,M. Giard,Y. Giraud-Héraud,Elena Giusarma,E. Gjerløw,J. González-Nuevo,Krzysztof M. Gorski,Serge Gratton,A. Gregorio,Alessandro Gruppuso,Jon E. Gudmundsson,Jan Hamann,F. K. Hansen,Duncan Hanson,D. L. Harrison,George Helou,Sophie Henrot-Versille,C. Hernández-Monteagudo,D. Herranz,S. R. Hildebrandt,E. Hivon,Michael P. Hobson,W. A. Holmes,Allan Hornstrup,W. Hovest,Zhiqi Huang,Kevin M. Huffenberger,G. Hurier,Andrew H. Jaffe,T. R. Jaffe,W. C. Jones,Mika Juvela,E. Keihänen,Reijo Keskitalo,Theodore Kisner,R. Kneissl,J. Knoche,Lloyd Knox,Martin Kunz,Hannu Kurki-Suonio,Guilaine Lagache,Anne Lähteenmäki,J.-M. Lamarre,Anthony Lasenby,Massimiliano Lattanzi,Charles R. Lawrence,J. P. Leahy,R. Leonardi,Julien Lesgourgues,François Levrier,Antony Lewis,Michele Liguori,P. B. Lilje,M. Linden-Vørnle,M. López-Caniego,Philip Lubin,J. F. Macías-Pérez,G. Maggio,Davide Maino,N. Mandolesi,A. Mangilli,A. Marchini,Peter G. Martin,M. Martinelli,E. Martínez-González,Silvia Masi,Sabino Matarrese,Pasquale Mazzotta,P. McGehee,Peter Meinhold,Alessandro Melchiorri,J.-B. Melin,L. Mendes,A. Mennella,M. Migliaccio,M. Millea,S. Mitra,M.-A. Miville-Deschênes,A. Moneti,L. Montier,Gianluca Morgante,Daniel J. Mortlock,Adam Moss,Dipak Munshi,J. A. Murphy,Pavel Naselsky,Federico Nati,Paolo Natoli,Calvin B. Netterfield,Hans Ulrik Nørgaard-Nielsen,F. Noviello,Dmitry Novikov,I. D. Novikov,C. A. Oxborrow,F. Paci,L. Pagano,F. Pajot,R. Paladini,Daniela Paoletti,Bruce Partridge,F. Pasian,G. Patanchon,T. J. Pearson,O. Perdereau,L. Perotto,Francesca Perrotta,Valeria Pettorino,F. Piacentini,M. Piat,E. Pierpaoli,Davide Pietrobon,Stéphane Plaszczynski,Etienne Pointecouteau,G. Polenta,L. Popa,G. W. Pratt,G. Prézeau,Simon Prunet,J.-L. Puget,Jörg P. Rachen,William T. Reach,Rafael Rebolo,M. Reinecke,Mathieu Remazeilles,C. Renault,A. Renzi,I. Ristorcelli,Graca Rocha,C. Rosset,M. Rossetti,G. Roudier,B. Rouillé d'Orfeuil,Michael Rowan-Robinson,Jose Alberto Rubino-Martin,Ben Rusholme,Najla Said,Valentina Salvatelli,L. Salvati,M. Sandri,D. Santos,M. Savelainen,Giorgio Savini,Douglas Scott,Michael Seiffert,Paolo Serra,E. P. S. Shellard,Locke D. Spencer,M. Spinelli,V. Stolyarov,R. Stompor,R. Sudiwala,R. A. Sunyaev,D. Sutton,A.-S. Suur-Uski,J.-F. Sygnet,J. A. Tauber,Luca Terenzi,L. Toffolatti,M. Tomasi,M. Tristram,T. Trombetti,M. Tucci,J. Tuovinen,M. Turler,G. Umana,Luca Valenziano,Jussi-Pekka Väliviita,B. Van Tent,P. Vielva,Fabrizio Villa,L. A. Wade,Benjamin D. Wandelt,Ingunn Kathrine Wehus,Martin White,Simon D. M. White,Althea Wilkinson,D. Yvon,Andrea Zacchei,Andrea Zonca +260 more
Cosmological parameters from CMB and other data: A Monte Carlo approach
Antony Lewis,Sarah Bridle +1 more
Efficient computation of CMB anisotropies in closed FRW models
Seven-year wilkinson microwave anisotropy probe (wmap *) observations: cosmological interpretation
Eiichiro Komatsu,Kristine M. Smith,Jo Dunkley,Charles L. Bennett,B. Gold,Gary Hinshaw,Norman Jarosik,Davin Larson,M. R. Nolta,Lyman A. Page,David N. Spergel,Mark Halpern,Robert S. Hill,A. Kogut,Michele Limon,S. S. Meyer,N. Odegard,Gregory S. Tucker,Janet Weiland,Edward J. Wollack,Edward L. Wright +20 more