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Advanced Markov Chain Monte Carlo Methods
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Book Synopsis Advanced Markov Chain Monte Carlo Methods by : Faming Liang
Download or read book Advanced Markov Chain Monte Carlo Methods written by Faming Liang and published by John Wiley & Sons. This book was released on 2011-07-05 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov Chain Monte Carlo (MCMC) methods are now an indispensable tool in scientific computing. This book discusses recent developments of MCMC methods with an emphasis on those making use of past sample information during simulations. The application examples are drawn from diverse fields such as bioinformatics, machine learning, social science, combinatorial optimization, and computational physics. Key Features: Expanded coverage of the stochastic approximation Monte Carlo and dynamic weighting algorithms that are essentially immune to local trap problems. A detailed discussion of the Monte Carlo Metropolis-Hastings algorithm that can be used for sampling from distributions with intractable normalizing constants. Up-to-date accounts of recent developments of the Gibbs sampler. Comprehensive overviews of the population-based MCMC algorithms and the MCMC algorithms with adaptive proposals. This book can be used as a textbook or a reference book for a one-semester graduate course in statistics, computational biology, engineering, and computer sciences. Applied or theoretical researchers will also find this book beneficial.
Book Synopsis Advanced Markov Chain Monte Carlo Methods by : Faming Liang
Download or read book Advanced Markov Chain Monte Carlo Methods written by Faming Liang and published by Wiley. This book was released on 2010-08-23 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov Chain Monte Carlo (MCMC) methods are now an indispensable tool in scientific computing. This book discusses recent developments of MCMC methods with an emphasis on those making use of past sample information during simulations. The application examples are drawn from diverse fields such as bioinformatics, machine learning, social science, combinatorial optimization, and computational physics. Key Features: Expanded coverage of the stochastic approximation Monte Carlo and dynamic weighting algorithms that are essentially immune to local trap problems. A detailed discussion of the Monte Carlo Metropolis-Hastings algorithm that can be used for sampling from distributions with intractable normalizing constants. Up-to-date accounts of recent developments of the Gibbs sampler. Comprehensive overviews of the population-based MCMC algorithms and the MCMC algorithms with adaptive proposals. This book can be used as a textbook or a reference book for a one-semester graduate course in statistics, computational biology, engineering, and computer sciences. Applied or theoretical researchers will also find this book beneficial.
Book Synopsis Markov Chain Monte Carlo Simulations and Their Statistical Analysis by : Bernd A Berg
Download or read book Markov Chain Monte Carlo Simulations and Their Statistical Analysis written by Bernd A Berg and published by World Scientific Publishing Company. This book was released on 2004-10-01 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book teaches modern Markov chain Monte Carlo (MC) simulation techniques step by step. The material should be accessible to advanced undergraduate students and is suitable for a course. It ranges from elementary statistics concepts (the theory behind MC simulations), through conventional Metropolis and heat bath algorithms, autocorrelations and the analysis of the performance of MC algorithms, to advanced topics including the multicanonical approach, cluster algorithms and parallel computing. Therefore, it is also of interest to researchers in the field. The book relates the theory directly to Web-based computer code. This allows readers to get quickly started with their own simulations and to verify many numerical examples easily. The present code is in Fortran 77, for which compilers are freely available. The principles taught are important for users of other programming languages, like C or C++.
Book Synopsis Handbook of Markov Chain Monte Carlo by : Steve Brooks
Download or read book Handbook of Markov Chain Monte Carlo written by Steve Brooks and published by CRC Press. This book was released on 2011-05-10 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their popularization in the 1990s, Markov chain Monte Carlo (MCMC) methods have revolutionized statistical computing and have had an especially profound impact on the practice of Bayesian statistics. Furthermore, MCMC methods have enabled the development and use of intricate models in an astonishing array of disciplines as diverse as fisherie
Book Synopsis MCMC from Scratch by : Masanori Hanada
Download or read book MCMC from Scratch written by Masanori Hanada and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explains the fundamentals of Markov Chain Monte Carlo (MCMC) without assuming advanced knowledge of mathematics and programming. MCMC is a powerful technique that can be used to integrate complicated functions or to handle complicated probability distributions. MCMC is frequently used in diverse fields where statistical methods are important - e.g. Bayesian statistics, quantum physics, machine learning, computer science, computational biology, and mathematical economics. This book aims to equip readers with a sound understanding of MCMC and enable them to write simulation codes by themselves. The content consists of six chapters. Following Chapter 2, which introduces readers to the Monte Carlo algorithm and highlights the advantages of MCMC, Chapter 3 presents the general aspects of MCMC. Chapter 4 illustrates the essence of MCMC through the simple example of the Metropolis algorithm. In turn, Chapter 5 explains the HMC algorithm, Gibbs sampling algorithm and Metropolis-Hastings algorithm, discussing their pros, cons and pitfalls. Lastly, Chapter 6 presents several applications of MCMC. Including a wealth of examples and exercises with solutions, as well as sample codes and further math topics in the Appendix, this book offers a valuable asset for students and beginners in various fields.
Book Synopsis Markov Chain Monte Carlo Simulations and Their Statistical Analysis by : Bernd A. Berg
Download or read book Markov Chain Monte Carlo Simulations and Their Statistical Analysis written by Bernd A. Berg and published by World Scientific. This book was released on 2004 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book teaches modern Markov chain Monte Carlo (MC) simulation techniques step by step. The material should be accessible to advanced undergraduate students and is suitable for a course. It ranges from elementary statistics concepts (the theory behind MC simulations), through conventional Metropolis and heat bath algorithms, autocorrelations and the analysis of the performance of MC algorithms, to advanced topics including the multicanonical approach, cluster algorithms and parallel computing. Therefore, it is also of interest to researchers in the field. The book relates the theory directly to Web-based computer code. This allows readers to get quickly started with their own simulations and to verify many numerical examples easily. The present code is in Fortran 77, for which compilers are freely available. The principles taught are important for users of other programming languages, like C or C++.
Book Synopsis Markov Chain Monte Carlo Methods in Quantum Field Theories by : Anosh Joseph
Download or read book Markov Chain Monte Carlo Methods in Quantum Field Theories written by Anosh Joseph and published by Springer Nature. This book was released on 2020-04-16 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is a comprehensive collection of analytical and numerical techniques that can be used to extract the non-perturbative physics of quantum field theories. The intriguing connection between Euclidean Quantum Field Theories (QFTs) and statistical mechanics can be used to apply Markov Chain Monte Carlo (MCMC) methods to investigate strongly coupled QFTs. The overwhelming amount of reliable results coming from the field of lattice quantum chromodynamics stands out as an excellent example of MCMC methods in QFTs in action. MCMC methods have revealed the non-perturbative phase structures, symmetry breaking, and bound states of particles in QFTs. The applications also resulted in new outcomes due to cross-fertilization with research areas such as AdS/CFT correspondence in string theory and condensed matter physics. The book is aimed at advanced undergraduate students and graduate students in physics and applied mathematics, and researchers in MCMC simulations and QFTs. At the end of this book the reader will be able to apply the techniques learned to produce more independent and novel research in the field.
Book Synopsis Markov Chain Monte Carlo in Practice by : W.R. Gilks
Download or read book Markov Chain Monte Carlo in Practice written by W.R. Gilks and published by CRC Press. This book was released on 1995-12-01 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a family study of breast cancer, epidemiologists in Southern California increase the power for detecting a gene-environment interaction. In Gambia, a study helps a vaccination program reduce the incidence of Hepatitis B carriage. Archaeologists in Austria place a Bronze Age site in its true temporal location on the calendar scale. And in France, researchers map a rare disease with relatively little variation. Each of these studies applied Markov chain Monte Carlo methods to produce more accurate and inclusive results. General state-space Markov chain theory has seen several developments that have made it both more accessible and more powerful to the general statistician. Markov Chain Monte Carlo in Practice introduces MCMC methods and their applications, providing some theoretical background as well. The authors are researchers who have made key contributions in the recent development of MCMC methodology and its application. Considering the broad audience, the editors emphasize practice rather than theory, keeping the technical content to a minimum. The examples range from the simplest application, Gibbs sampling, to more complex applications. The first chapter contains enough information to allow the reader to start applying MCMC in a basic way. The following chapters cover main issues, important concepts and results, techniques for implementing MCMC, improving its performance, assessing model adequacy, choosing between models, and applications and their domains. Markov Chain Monte Carlo in Practice is a thorough, clear introduction to the methodology and applications of this simple idea with enormous potential. It shows the importance of MCMC in real applications, such as archaeology, astronomy, biostatistics, genetics, epidemiology, and image analysis, and provides an excellent base for MCMC to be applied to other fields as well.
Book Synopsis Monte Carlo Methods in Bayesian Computation by : Ming-Hui Chen
Download or read book Monte Carlo Methods in Bayesian Computation written by Ming-Hui Chen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dealing with methods for sampling from posterior distributions and how to compute posterior quantities of interest using Markov chain Monte Carlo (MCMC) samples, this book addresses such topics as improving simulation accuracy, marginal posterior density estimation, estimation of normalizing constants, constrained parameter problems, highest posterior density interval calculations, computation of posterior modes, and posterior computations for proportional hazards models and Dirichlet process models. The authors also discuss model comparisons, including both nested and non-nested models, marginal likelihood methods, ratios of normalizing constants, Bayes factors, the Savage-Dickey density ratio, Stochastic Search Variable Selection, Bayesian Model Averaging, the reverse jump algorithm, and model adequacy using predictive and latent residual approaches. The book presents an equal mixture of theory and applications involving real data, and is intended as a graduate textbook or a reference book for a one-semester course at the advanced masters or Ph.D. level. It will also serve as a useful reference for applied or theoretical researchers as well as practitioners.
Book Synopsis Introducing Monte Carlo Methods with R by : Christian Robert
Download or read book Introducing Monte Carlo Methods with R written by Christian Robert and published by Springer Science & Business Media. This book was released on 2010 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the main tools used in statistical simulation from a programmer’s point of view, explaining the R implementation of each simulation technique and providing the output for better understanding and comparison.
Book Synopsis Markov Chain Monte Carlo by : Dani Gamerman
Download or read book Markov Chain Monte Carlo written by Dani Gamerman and published by CRC Press. This book was released on 2006-05-10 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: While there have been few theoretical contributions on the Markov Chain Monte Carlo (MCMC) methods in the past decade, current understanding and application of MCMC to the solution of inference problems has increased by leaps and bounds. Incorporating changes in theory and highlighting new applications, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition presents a concise, accessible, and comprehensive introduction to the methods of this valuable simulation technique. The second edition includes access to an internet site that provides the code, written in R and WinBUGS, used in many of the previously existing and new examples and exercises. More importantly, the self-explanatory nature of the codes will enable modification of the inputs to the codes and variation on many directions will be available for further exploration. Major changes from the previous edition: · More examples with discussion of computational details in chapters on Gibbs sampling and Metropolis-Hastings algorithms · Recent developments in MCMC, including reversible jump, slice sampling, bridge sampling, path sampling, multiple-try, and delayed rejection · Discussion of computation using both R and WinBUGS · Additional exercises and selected solutions within the text, with all data sets and software available for download from the Web · Sections on spatial models and model adequacy The self-contained text units make MCMC accessible to scientists in other disciplines as well as statisticians. The book will appeal to everyone working with MCMC techniques, especially research and graduate statisticians and biostatisticians, and scientists handling data and formulating models. The book has been substantially reinforced as a first reading of material on MCMC and, consequently, as a textbook for modern Bayesian computation and Bayesian inference courses.
Book Synopsis Markov Chain Monte Carlo by : Dani Gamerman
Download or read book Markov Chain Monte Carlo written by Dani Gamerman and published by CRC Press. This book was released on 1997-10-01 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the gap between research and application, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference provides a concise, and integrated account of Markov chain Monte Carlo (MCMC) for performing Bayesian inference. This volume, which was developed from a short course taught by the author at a meeting of Brazilian statisticians and probabilists, retains the didactic character of the original course text. The self-contained text units make MCMC accessible to scientists in other disciplines as well as statisticians. It describes each component of the theory in detail and outlines related software, which is of particular benefit to applied scientists.
Book Synopsis Markov Chain Monte Carlo by : W S Kendall
Download or read book Markov Chain Monte Carlo written by W S Kendall and published by World Scientific. This book was released on 2005-11-08 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov Chain Monte Carlo (MCMC) originated in statistical physics, but has spilled over into various application areas, leading to a corresponding variety of techniques and methods. That variety stimulates new ideas and developments from many different places, and there is much to be gained from cross-fertilization. This book presents five expository essays by leaders in the field, drawing from perspectives in physics, statistics and genetics, and showing how different aspects of MCMC come to the fore in different contexts. The essays derive from tutorial lectures at an interdisciplinary program at the Institute for Mathematical Sciences, Singapore, which exploited the exciting ways in which MCMC spreads across different disciplines. Contents:Introduction to Markov Chain Monte Carlo Simulations and Their Statistical Analysis (B A Berg)An Introduction to Monte Carlo Methods in Statistical Physics (D P Landau)Notes on Perfect Simulation (W S Kendall)Sequential Monte Carlo Methods and Their Applications (R Chen)MCMC in the Analysis of Genetic Data on Pedigrees (E A Thompson) Readership: Academic researchers in physics, statistics and bioinformatics. Keywords:Markov Chain Monte Carlo;Simulation Physics;Genetics;Perfect Simulation;Sequential Monte CarloKey Features:Exposition at graduate student level forms an excellent introduction for beginning PhD studentsContains descriptions of the latest simulation physics techniques in MCMCPresents a survey of perfect simulation methodsProvides a careful treatment of sequential methodsIncludes a case study of MCMC applied in genetics
Download or read book Markov Chains written by Pierre Bremaud and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling. However it is motivated by significant applications and progressively brings the student to the borders of contemporary research. Examples are from a wide range of domains, including operations research and electrical engineering. Researchers and students in these areas as well as in physics, biology and the social sciences will find this book of interest.
Book Synopsis Handbook of Monte Carlo Methods by : Dirk P. Kroese
Download or read book Handbook of Monte Carlo Methods written by Dirk P. Kroese and published by John Wiley & Sons. This book was released on 2013-06-06 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications More and more of today’s numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field. The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including: Random variable and stochastic process generation Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run Discrete-event simulation Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo Estimation of derivatives and sensitivity analysis Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization The presented theoretical concepts are illustrated with worked examples that use MATLAB®, a related Web site houses the MATLAB® code, allowing readers to work hands-on with the material and also features the author's own lecture notes on Monte Carlo methods. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation. Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research. It is also a suitable supplement for courses on Monte Carlo methods and computational statistics at the upper-undergraduate and graduate levels.
Download or read book Markov Chains written by Randal Douc and published by Springer. This book was released on 2018-12-11 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the classical theory of Markov chains on general state-spaces as well as many recent developments. The theoretical results are illustrated by simple examples, many of which are taken from Markov Chain Monte Carlo methods. The book is self-contained, while all the results are carefully and concisely proven. Bibliographical notes are added at the end of each chapter to provide an overview of the literature. Part I lays the foundations of the theory of Markov chain on general states-space. Part II covers the basic theory of irreducible Markov chains on general states-space, relying heavily on regeneration techniques. These two parts can serve as a text on general state-space applied Markov chain theory. Although the choice of topics is quite different from what is usually covered, where most of the emphasis is put on countable state space, a graduate student should be able to read almost all these developments without any mathematical background deeper than that needed to study countable state space (very little measure theory is required). Part III covers advanced topics on the theory of irreducible Markov chains. The emphasis is on geometric and subgeometric convergence rates and also on computable bounds. Some results appeared for a first time in a book and others are original. Part IV are selected topics on Markov chains, covering mostly hot recent developments.
Book Synopsis An Introduction to Sequential Monte Carlo by : Nicolas Chopin
Download or read book An Introduction to Sequential Monte Carlo written by Nicolas Chopin and published by Springer Nature. This book was released on 2020-10-01 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a general introduction to Sequential Monte Carlo (SMC) methods, also known as particle filters. These methods have become a staple for the sequential analysis of data in such diverse fields as signal processing, epidemiology, machine learning, population ecology, quantitative finance, and robotics. The coverage is comprehensive, ranging from the underlying theory to computational implementation, methodology, and diverse applications in various areas of science. This is achieved by describing SMC algorithms as particular cases of a general framework, which involves concepts such as Feynman-Kac distributions, and tools such as importance sampling and resampling. This general framework is used consistently throughout the book. Extensive coverage is provided on sequential learning (filtering, smoothing) of state-space (hidden Markov) models, as this remains an important application of SMC methods. More recent applications, such as parameter estimation of these models (through e.g. particle Markov chain Monte Carlo techniques) and the simulation of challenging probability distributions (in e.g. Bayesian inference or rare-event problems), are also discussed. The book may be used either as a graduate text on Sequential Monte Carlo methods and state-space modeling, or as a general reference work on the area. Each chapter includes a set of exercises for self-study, a comprehensive bibliography, and a “Python corner,” which discusses the practical implementation of the methods covered. In addition, the book comes with an open source Python library, which implements all the algorithms described in the book, and contains all the programs that were used to perform the numerical experiments.
