Journal ArticleDOI
A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: easy Bayesian computing for real parameter spaces
TLDR
The essential ideas of DE and MCMC are integrated, resulting in Differential Evolution Markov Chain (DE-MC), a population MCMC algorithm, in which multiple chains are run in parallel, showing simplicity, speed of calculation and convergence, even for nearly collinear parameters and multimodal densities.Abstract:
Differential Evolution (DE) is a simple genetic algorithm for numerical optimization in real parameter spaces. In a statistical context one would not just want the optimum but also its uncertainty. The uncertainty distribution can be obtained by a Bayesian analysis (after specifying prior and likelihood) using Markov Chain Monte Carlo (MCMC) simulation. This paper integrates the essential ideas of DE and MCMC, resulting in Differential Evolution Markov Chain (DE-MC). DE-MC is a population MCMC algorithm, in which multiple chains are run in parallel. DE-MC solves an important problem in MCMC, namely that of choosing an appropriate scale and orientation for the jumping distribution. In DE-MC the jumps are simply a fixed multiple of the differences of two random parameter vectors that are currently in the population. The selection process of DE-MC works via the usual Metropolis ratio which defines the probability with which a proposal is accepted. In tests with known uncertainty distributions, the efficiency of DE-MC with respect to random walk Metropolis with optimal multivariate Normal jumps ranged from 68% for small population sizes to 100% for large population sizes and even to 500% for the 97.5% point of a variable from a 50-dimensional Student distribution. Two Bayesian examples illustrate the potential of DE-MC in practice. DE-MC is shown to facilitate multidimensional updates in a multi-chain "Metropolis-within-Gibbs" sampling approach. The advantage of DE-MC over conventional MCMC are simplicity, speed of calculation and convergence, even for nearly collinear parameters and multimodal densities.read more
Citations
More filters
Stan: A Probabilistic Programming Language.
Bob Carpenter,Andrew Gelman,Matthew D. Hoffman,Daniel D. Lee,Ben Goodrich,Michael Betancourt,Marcus A. Brubaker,Jiqiang Guo,Peter Li,Allen Riddell +9 more
TL;DR: Stan is a probabilistic programming language for specifying statistical models that provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler and an adaptive form of Hamiltonian Monte Carlo sampling.
Journal ArticleDOI
Estimated transmissibility and impact of SARS-CoV-2 lineage B.1.1.7 in England.
Nicholas G Davies,Sam Abbott,Rosanna C. Barnard,Christopher I Jarvis,Adam J. Kucharski,James D Munday,Carl A. B. Pearson,Timothy W Russell,Damien C. Tully,Alex D. Washburne,Tom Wenseleers,Amy Gimma,William Waites,Kerry L. M. Wong,Kevin van Zandvoort,Justin D. Silverman,Karla Diaz-Ordaz,Ruth H. Keogh,Rosalind M Eggo,Sebastian Funk,Mark Jit,Katherine E. Atkins,Katherine E. Atkins,W. John Edmunds +23 more
TL;DR: Using a variety of statistical and dynamic modeling approaches, the authors estimate that this variant has a 43 to 90% (range of 95% credible intervals, 38 to 130%) higher reproduction number than preexisting variants, and a fitted two-strain dynamic transmission model shows that VOC 202012/01 will lead to large resurgences of COVID-19 cases.
Journal ArticleDOI
Age-dependent effects in the transmission and control of COVID-19 epidemics.
TL;DR: It is found that interventions aimed at children might have a relatively small impact on reducing SARS-CoV-2 transmission, particularly if the transmissibility of subclinical infections is low.
Journal ArticleDOI
First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
Kazunori Akiyama,Antxon Alberdi,Walter Alef,Keiichi Asada,Rebecca Azulay,Rebecca Azulay,Anne Kathrin Baczko,David Ball,Mislav Baloković,Mislav Baloković,John E. Barrett,Dan Bintley,Lindy Blackburn,Lindy Blackburn,W. Boland,Katherine L. Bouman,Katherine L. Bouman,Katherine L. Bouman,Geoffrey C. Bower,Michael Bremer,Christiaan D. Brinkerink,Roger Brissenden,Roger Brissenden,Silke Britzen,Avery E. Broderick,Avery E. Broderick,Dominique Broguiere,Thomas Bronzwaer,Do-Young Byun,John E. Carlstrom,Andrew Chael,Andrew Chael,Chi-kwan Chan,Shami Chatterjee,Koushik Chatterjee,Ming-Tang Chen,Yi Chen,Ilje Cho,Pierre Christian,Pierre Christian,John Conway,James M. Cordes,Geoffrey B. Crew,Yuzhu Cui,Jordy Davelaar,Mariafelicia De Laurentis,Roger Deane,Roger Deane,Jessica Dempsey,Gregory Desvignes,Jason Dexter,Sheperd S. Doeleman,Sheperd S. Doeleman,R. P. Eatough,Heino Falcke,Vincent L. Fish,Ed Fomalont,Raquel Fraga-Encinas,Per Friberg,Christian M. Fromm,José L. Gómez,Peter Galison,Charles F. Gammie,Roberto Garcia,Olivier Gentaz,Boris Georgiev,Ciriaco Goddi,Ciriaco Goddi,Roman Gold,Minfeng Gu,Mark Gurwell,Kazuhiro Hada,Michael H. Hecht,Ronald Hesper,Luis C. Ho,Paul T. P. Ho,Mareki Honma,Chih-Wei Locutus Huang,Lei Huang,David H. Hughes,Shiro Ikeda,Makoto Inoue,Sara Issaoun,David J. James,David J. James,Buell T. Jannuzi,Michael Janssen,Britton Jeter,Wu Jiang,Michael D. Johnson,Michael D. Johnson,Svetlana G. Jorstad,Svetlana G. Jorstad,Taehyun Jung,Mansour Karami,Mansour Karami,Ramesh Karuppusamy,Tomohisa Kawashima,Garrett K. Keating,Mark Kettenis,Jae-Young Kim,Junhan Kim,Jongsoo Kim,Motoki Kino,Jun Yi Koay,Patrick M. Koch,Shoko Koyama,Michael Kramer,Carsten Kramer,Thomas P. Krichbaum,C. Y. Kuo,Tod R. Lauer,Sang-Sung Lee,Yan-Rong Li,Zhiyuan Li,Michael Lindqvist,Kuo Liu,Elisabetta Liuzzo,Wen Ping Lo,Wen Ping Lo,Andrei P. Lobanov,Laurent Loinard,Colin J. Lonsdale,Ru-Sen Lu,Ru-Sen Lu,Nicholas R. MacDonald,Jirong Mao,Sera Markoff,Daniel P. Marrone,Alan P. Marscher,Ivan Marti-Vidal,Satoki Matsushita,Lynn D. Matthews,Lia Medeiros,Lia Medeiros,Karl M. Menten,Yosuke Mizuno,Izumi Mizuno,James M. Moran,James M. Moran,Kotaro Moriyama,Monika Moscibrodzka,Cornelia Müller,Cornelia Müller,Hiroshi Nagai,Neil M. Nagar,Masanori Nakamura,Ramesh Narayan,Ramesh Narayan,Gopal Narayanan,Iniyan Natarajan,Roberto Neri,Chunchong Ni,Aristeidis Noutsos,Hiroki Okino,Hector Olivares,Tomoaki Oyama,Feryal Özel,Daniel C. M. Palumbo,Daniel C. M. Palumbo,Nimesh A. Patel,Ue-Li Pen,Dominic W. Pesce,Dominic W. Pesce,Vincent Piétu,Richard L. Plambeck,Aleksandar Popstefanija,Oliver Porth,Oliver Porth,Ben Prather,Jorge A. Preciado-López,Dimitrios Psaltis,Hung Yi Pu,Venkatessh Ramakrishnan,Ramprasad Rao,Mark G. Rawlings,Alexander W. Raymond,Alexander W. Raymond,Luciano Rezzolla,Bart Ripperda,Freek Roelofs,Alan E. E. Rogers,Eduardo Ros,Mel Rose,Arash Roshanineshat,Helge Rottmann,Alan L. Roy,Chet Ruszczyk,Benjamin R. Ryan,Kazi L.J. Rygl,S. Sánchez,David Sánchez-Arguelles,David Sánchez-Arguelles,Mahito Sasada,Tuomas Savolainen,Tuomas Savolainen,F. Peter Schloerb,Karl Friedrich Schuster,Lijing Shao,Lijing Shao,Zhiqiang Shen,Des Small,Bong Won Sohn,Bong Won Sohn,Jason SooHoo,Fumie Tazaki,Paul Tiede,Remo P. J. Tilanus,Remo P. J. Tilanus,Remo P. J. Tilanus,Michael Titus,Kenji Toma,Pablo Torne,Tyler Trent,Sascha Trippe,Shuichiro Tsuda,Ilse van Bemmel,Huib Jan van Langevelde,Huib Jan van Langevelde,Daniel R. van Rossum,Jan Wagner,John Wardle,Jonathan Weintroub,Jonathan Weintroub,Norbert Wex,Robert Wharton,Maciek Wielgus,Maciek Wielgus,George N. Wong,Qingwen Wu,André Young,Ken H. Young,Ziri Younsi,Ziri Younsi,Feng Yuan,Ye-Fei Yuan,J. Anton Zensus,Guang-Yao Zhao,Shan Shan Zhao,Shan Shan Zhao,Ziyan Zhu,Joseph R. Farah,Joseph R. Farah,Joseph R. Farah,Zheng Meyer-Zhao,Zheng Meyer-Zhao,Daniel Michalik,Daniel Michalik,A. Nadolski,Hiroaki Nishioka,Nicolas Pradel,Rurik A. Primiani,Kamal Souccar,Laura Vertatschitsch,Paul Yamaguchi +254 more
TL;DR: In this article, the authors present measurements of the properties of the central radio source in M87 using Event Horizon Telescope data obtained during the 2017 campaign, and find that >50% of the total flux at arcsecond scales comes from near the horizon and that the emission is dramatically suppressed interior to this region by a factor >10, providing direct evidence of the predicted shadow of a black hole.
Journal ArticleDOI
Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling
TL;DR: The DREAM scheme significantly enhances the applicability of MCMC simulation to complex, multi-modal search problems andErgodicity of the algorithm is proved, and various examples involving nonlinearity, high-dimensionality, and multimodality show that DREAM is generally superior to other adaptive MCMC sampling approaches.
References
More filters
Journal ArticleDOI
Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces
Rainer Storn,Kenneth Price +1 more
TL;DR: In this article, a new heuristic approach for minimizing possibly nonlinear and non-differentiable continuous space functions is presented, which requires few control variables, is robust, easy to use, and lends itself very well to parallel computation.
Book
Bayesian Data Analysis
TL;DR: Detailed notes on Bayesian Computation Basics of Markov Chain Simulation, Regression Models, and Asymptotic Theorems are provided.
Book
Mixed-Effects Models in S and S-PLUS
TL;DR: Linear Mixed-Effects and Nonlinear Mixed-effects (NLME) models have been studied in the literature as mentioned in this paper, where the structure of grouped data has been used for fitting LME models.
BookDOI
Markov Chain Monte Carlo in Practice
TL;DR: The Markov Chain Monte Carlo Implementation Results Summary and Discussion MEDICAL MONITORING Introduction Modelling Medical Monitoring Computing Posterior Distributions Forecasting Model Criticism Illustrative Application Discussion MCMC for NONLINEAR HIERARCHICAL MODELS.
Book
Monte Carlo Statistical Methods
TL;DR: This new edition contains five completely new chapters covering new developments and has sold 4300 copies worldwide of the first edition (1999).
Related Papers (5)
Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces
Rainer Storn,Kenneth Price +1 more