Random Number Generation And Monte Carlo Methods
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Random Number Generation And Monte Carlo Methods
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Author : James E. Gentle
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
Random Number Generation And Monte Carlo Methods written by James E. Gentle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-18 with Computers categories.
Monte Carlo simulation has become one of the most important tools in all fields of science. Simulation methodology relies on a good source of numbers that appear to be random. These "pseudorandom" numbers must pass statistical tests just as random samples would. Methods for producing pseudorandom numbers and transforming those numbers to simulate samples from various distributions are among the most important topics in statistical computing. This book surveys techniques of random number generation and the use of random numbers in Monte Carlo simulation. The book covers basic principles, as well as newer methods such as parallel random number generation, nonlinear congruential generators, quasi Monte Carlo methods, and Markov chain Monte Carlo. The best methods for generating random variates from the standard distributions are presented, but also general techniques useful in more complicated models and in novel settings are described. The emphasis throughout the book is on practical methods that work well in current computing environments. The book includes exercises and can be used as a test or supplementary text for various courses in modern statistics. It could serve as the primary test for a specialized course in statistical computing, or as a supplementary text for a course in computational statistics and other areas of modern statistics that rely on simulation. The book, which covers recent developments in the field, could also serve as a useful reference for practitioners. Although some familiarity with probability and statistics is assumed, the book is accessible to a broad audience. The second edition is approximately 50% longer than the first edition. It includes advances in methods for parallel random number generation, universal methods for generation of nonuniform variates, perfect sampling, and software for random number generation.
Random Number Generation And Monte Carlo Methods
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Author : James E. Gentle
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Random Number Generation And Monte Carlo Methods written by James E. Gentle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Computers categories.
The role of Monte Carlo methods and simulation in all of the sciences has in creased in importance during the past several years. These methods are at the heart of the rapidly developing subdisciplines of computational physics, compu tational chemistry, and the other computational sciences. The growing power of computers and the evolving simulation methodology have led to the recog nition of computation as a third approach for advancing the natural sciences, together with theory and traditional experimentation. Monte Carlo is also a fundamental tool of computational statistics. At the kernel of a Monte Carlo or simulation method is random number generation. Generation of random numbers is also at the heart of many standard statis tical methods. The random sampling required in most analyses is usually done by the computer. The computations required in Bayesian analysis have become viable because of Monte Carlo methods. This has led to much wider applications of Bayesian statistics, which, in turn, has led to development of new Monte Carlo methods and to refinement of existing procedures for random number generation.
Monte Carlo Methods
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Author : Malvin H. Kalos
language : en
Publisher: John Wiley & Sons
Release Date : 2009-06-10
Monte Carlo Methods written by Malvin H. Kalos and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-10 with Science categories.
This introduction to Monte Carlo methods seeks to identify and study the unifying elements that underlie their effective application. Initial chapters provide a short treatment of the probability and statistics needed as background, enabling those without experience in Monte Carlo techniques to apply these ideas to their research. The book focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modeling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on this example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrödinger equation by random walks. The text includes sample problems that readers can solve by themselves to illustrate the content of each chapter. This is the second, completely revised and extended edition of the successful monograph, which brings the treatment up to date and incorporates the many advances in Monte Carlo techniques and their applications, while retaining the original elementary but general approach.
Random Number Generation And Monte Carlo Methods
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Author : Springer
language : en
Publisher:
Release Date : 2014-01-15
Random Number Generation And Monte Carlo Methods written by Springer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Handbook Of Monte Carlo Methods
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Author : Dirk P. Kroese
language : en
Publisher: John Wiley & Sons
Release Date : 2013-06-06
Handbook Of Monte Carlo Methods written by Dirk P. Kroese and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-06 with Mathematics categories.
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.
Matrix Algebra
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Author : James E. Gentle
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-06
Matrix Algebra written by James E. Gentle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-06 with Mathematics categories.
Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, next covers the basic algebraic properties of matrices, then describes the analytic properties of vectors and matrices in the multivariate calculus, and finally discusses operations on matrices in solutions of linear systems and in eigenanalysis. This part is essentially self-contained. The second part of the book begins with a consideration of various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. The second part also describes some of the many applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. The brief coverage in this part illustrates the matrix theory developed in the first part of the book. The first two parts of the book can be used as the text for a course in matrix algebra for statistics students, or as a supplementary text for various courses in linear models or multivariate statistics. The third part of this book covers numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. This part is essentially self-contained, although it assumes some ability to program in Fortran or C and/or the ability to use R/S-Plus or Matlab. This part of the book can be used as the text for a course in statistical computing, or as a supplementary text for various courses that emphasize computations. The book includes a large number of exercises with some solutions provided in an appendix.
Exploring Monte Carlo Methods
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Author : William L. Dunn
language : en
Publisher: Elsevier
Release Date : 2022-06-07
Exploring Monte Carlo Methods written by William L. Dunn and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-07 with Science categories.
Exploring Monte Carlo Methods, Second Edition provides a valuable introduction to the numerical methods that have come to be known as "Monte Carlo." This unique and trusted resource for course use, as well as researcher reference, offers accessible coverage, clear explanations and helpful examples throughout. Building from the basics, the text also includes applications in a variety of fields, such as physics, nuclear engineering, finance and investment, medical modeling and prediction, archaeology, geology and transportation planning. - Provides a comprehensive yet concise treatment of Monte Carlo methods - Uses the famous "Buffon's needle problem" as a unifying theme to illustrate the many aspects of Monte Carlo methods - Includes numerous exercises and useful appendices on: Certain mathematical functions, Bose Einstein functions, Fermi Dirac functions and Watson functions
Monte Carlo And Quasi Monte Carlo Methods 2000
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Author : Kai-Tai Fang
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28
Monte Carlo And Quasi Monte Carlo Methods 2000 written by Kai-Tai Fang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Mathematics categories.
This book represents the refereed proceedings of the Fourth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at Hong Kong Baptist University in 2000. An important feature are invited surveys of the state-of-the-art in key areas such as multidimensional numerical integration, low-discrepancy point sets, random number generation, and applications of Monte Carlo and quasi-Monte Carlo methods. These proceedings include also carefully selected contributed papers on all aspects of Monte Carlo and quasi-Monte Carlo methods. The reader will be informed about current research in this very active field.
Quantum Monte Carlo Methods In Physics And Chemistry
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Author : M.P. Nightingale
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-12-31
Quantum Monte Carlo Methods In Physics And Chemistry written by M.P. Nightingale and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-31 with Science categories.
In recent years there has been a considerable growth in interest in Monte Carlo methods, and quantum Monte Carlo methods in particlular. Clearly, the ever-increasing computational power available to researchers, has stimulated the development of improved algorithms, and almost all fields in computational physics and chemistry are affected by their applications. Here we just mention some fields that are covered in the lecture notes contained in this volume, viz. electronic structure studies of atoms, molecules and solids, nuclear structure, and low- or zero-temperature studies of strongly-correlated quantum systems, both of the continuum and lattice variety, and cooperative phenomena in classical systems. Although each area of application may have its own peculiarities, requiring specialized solutions, all share the same basic methodology. It was with the intention of bringing together researchers and students from these various areas that the NATO Advanced Study Institute on Quantum Monte Carlo Methods in Physics and Chemistry was held at Cornell University from 12 to 24 July, 1998. This book contains material presented at the Institute in a series of mini courses in quantum Monte Carlo methods. The program consisted of lectures predominantly of a pedagogical nature, and of more specialized seminars. The levels varied from introductory to advanced, and from basic methods to applications; the program was intended for an audience working towards the Ph.D. level and above. Despite the essentially pedagogic nature of the Institute, several of the lectures and seminars contained in this volume present recent developments not previously published.
Monte Carlo And Quasi Monte Carlo Methods
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Author : Aicke Hinrichs
language : en
Publisher: Springer Nature
Release Date : 2024-07-12
Monte Carlo And Quasi Monte Carlo Methods written by Aicke Hinrichs and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-12 with Mathematics categories.
This book presents the refereed proceedings of the 15th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held in Linz, Austria, and organized by the Johannes Kepler University Linz and the Austrian Academy of Sciences, in July 2022. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these highly active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, in particular arising in finance, statistics and computer graphics.