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The Monte Carlo Method
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Book Synopsis Monte Carlo Methods by : Adrian Barbu
Download or read book Monte Carlo Methods written by Adrian Barbu and published by Springer Nature. This book was released on 2020-02-24 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to bridge the gap between statistics and computer science. It provides an overview of Monte Carlo methods, including Sequential Monte Carlo, Markov Chain Monte Carlo, Metropolis-Hastings, Gibbs Sampler, Cluster Sampling, Data Driven MCMC, Stochastic Gradient descent, Langevin Monte Carlo, Hamiltonian Monte Carlo, and energy landscape mapping. Due to its comprehensive nature, the book is suitable for developing and teaching graduate courses on Monte Carlo methods. To facilitate learning, each chapter includes several representative application examples from various fields. The book pursues two main goals: (1) It introduces researchers to applying Monte Carlo methods to broader problems in areas such as Computer Vision, Computer Graphics, Machine Learning, Robotics, Artificial Intelligence, etc.; and (2) it makes it easier for scientists and engineers working in these areas to employ Monte Carlo methods to enhance their research.
Book Synopsis Monte Carlo Methods by : Malvin H. Kalos
Download or read book Monte Carlo Methods written by Malvin H. Kalos and published by John Wiley & Sons. This book was released on 2008-09-26 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Monte Carlo Methods seeks to identify and study the unifying elements that underlie their effective application. It 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 modelling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on that 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 Schrodinger equation by random walks. The detailed discussion of variance reduction includes Monte Carlo evaluation of finite-dimensional integrals. Special attention is given to importance sampling, partly because of its intrinsic interest in quadrature, partly because of its general usefulness in the solution of integral equations. One significant feature is that Monte Carlo Methods treats the "Metropolis algorithm" in the context of sampling methods, clearly distinguishing it from importance sampling. Physicists, chemists, statisticians, mathematicians, and computer scientists will find Monte Carlo Methods a complete and stimulating introduction.
Book Synopsis Simulation and the Monte Carlo Method by : Reuven Y. Rubinstein
Download or read book Simulation and the Monte Carlo Method written by Reuven Y. Rubinstein and published by John Wiley & Sons. This book was released on 2016-10-21 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible new edition explores the major topics in Monte Carlo simulation that have arisen over the past 30 years and presents a sound foundation for problem solving Simulation and the Monte Carlo Method, Third Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the state-of-the-art theory, methods and applications that have emerged in Monte Carlo simulation since the publication of the classic First Edition over more than a quarter of a century ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo, variance reduction techniques such as importance (re-)sampling, and the transform likelihood ratio method, the score function method for sensitivity analysis, the stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization, the cross-entropy method for rare events estimation and combinatorial optimization, and application of Monte Carlo techniques for counting problems. An extensive range of exercises is provided at the end of each chapter, as well as a generous sampling of applied examples. The Third Edition features a new chapter on the highly versatile splitting method, with applications to rare-event estimation, counting, sampling, and optimization. A second new chapter introduces the stochastic enumeration method, which is a new fast sequential Monte Carlo method for tree search. In addition, the Third Edition features new material on: • Random number generation, including multiple-recursive generators and the Mersenne Twister • Simulation of Gaussian processes, Brownian motion, and diffusion processes • Multilevel Monte Carlo method • New enhancements of the cross-entropy (CE) method, including the “improved” CE method, which uses sampling from the zero-variance distribution to find the optimal importance sampling parameters • Over 100 algorithms in modern pseudo code with flow control • Over 25 new exercises Simulation and the Monte Carlo Method, Third Edition is an excellent text for upper-undergraduate and beginning graduate courses in stochastic simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method. Reuven Y. Rubinstein, DSc, was Professor Emeritus in the Faculty of Industrial Engineering and Management at Technion-Israel Institute of Technology. He served as a consultant at numerous large-scale organizations, such as IBM, Motorola, and NEC. The author of over 100 articles and six books, Dr. Rubinstein was also the inventor of the popular score-function method in simulation analysis and generic cross-entropy methods for combinatorial optimization and counting. Dirk P. Kroese, PhD, is a Professor of Mathematics and Statistics in the School of Mathematics and Physics of The University of Queensland, Australia. He has published over 100 articles and four books in a wide range of areas in applied probability and statistics, including Monte Carlo methods, cross-entropy, randomized algorithms, tele-traffic c theory, reliability, computational statistics, applied probability, and stochastic modeling.
Book Synopsis Monte Carlo Simulation and Resampling Methods for Social Science by : Thomas M. Carsey
Download or read book Monte Carlo Simulation and Resampling Methods for Social Science written by Thomas M. Carsey and published by SAGE Publications. This book was released on 2013-08-05 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking the topics of a quantitative methodology course and illustrating them through Monte Carlo simulation, this book examines abstract principles, such as bias, efficiency, and measures of uncertainty in an intuitive, visual way. Instead of thinking in the abstract about what would happen to a particular estimator "in repeated samples," the book uses simulation to actually create those repeated samples and summarize the results. The book includes basic examples appropriate for readers learning the material for the first time, as well as more advanced examples that a researcher might use to evaluate an estimator he or she was using in an actual research project. The book also covers a wide range of topics related to Monte Carlo simulation, such as resampling methods, simulations of substantive theory, simulation of quantities of interest (QI) from model results, and cross-validation. Complete R code from all examples is provided so readers can replicate every analysis presented using R.
Book Synopsis Monte Carlo Methods in Financial Engineering by : Paul Glasserman
Download or read book Monte Carlo Methods in Financial Engineering written by Paul Glasserman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis
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.
Book Synopsis Essentials of Monte Carlo Simulation by : Nick T. Thomopoulos
Download or read book Essentials of Monte Carlo Simulation written by Nick T. Thomopoulos and published by Springer Science & Business Media. This book was released on 2012-12-19 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essentials of Monte Carlo Simulation focuses on the fundamentals of Monte Carlo methods using basic computer simulation techniques. The theories presented in this text deal with systems that are too complex to solve analytically. As a result, readers are given a system of interest and constructs using computer code, as well as algorithmic models to emulate how the system works internally. After the models are run several times, in a random sample way, the data for each output variable(s) of interest is analyzed by ordinary statistical methods. This book features 11 comprehensive chapters, and discusses such key topics as random number generators, multivariate random variates, and continuous random variates. Over 100 numerical examples are presented as part of the appendix to illustrate useful real world applications. The text also contains an easy to read presentation with minimal use of difficult mathematical concepts. Very little has been published in the area of computer Monte Carlo simulation methods, and this book will appeal to students and researchers in the fields of Mathematics and Statistics.
Book Synopsis Quantum Monte Carlo Methods by : James Gubernatis
Download or read book Quantum Monte Carlo Methods written by James Gubernatis and published by Cambridge University Press. This book was released on 2016-06-02 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and researchers interested in quantum Monte Carlo techniques.
Book Synopsis The Monte Carlo Methods in Atmospheric Optics by : G.I. Marchuk
Download or read book The Monte Carlo Methods in Atmospheric Optics written by G.I. Marchuk and published by Springer. This book was released on 2013-04-17 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to urgent questions of the theory and applications of the Monte Carlo method for solving problems of atmospheric optics and hydrooptics. The importance of these problems has grown because of the increas ing need to interpret optical observations, and to estimate radiative balance precisely for weather forecasting. Inhomogeneity and sphericity of the atmos phere, absorption in atmospheric layers, multiple scattering and polarization of light, all create difficulties in solving these problems by traditional methods of computational mathematics. Particular difficulty arises when one must solve nonstationary problems of the theory of transfer of narrow beams that are connected with the estimation of spatial location and time characteristics of the radiation field. The most universal method for solving those problems is the Monte Carlo method, which is a numerical simulation of the radiative-transfer process. This process can be regarded as a Markov chain of photon collisions in a medium, which result in scattering or absorption. The Monte Carlo tech nique consists in computational simulation of that chain and in constructing statistical estimates of the desired functionals. The authors of this book have contributed to the development of mathemati cal methods of simulation and to the interpretation of optical observations. A series of general method using Monte Carlo techniques has been developed. The present book includes theories and algorithms of simulation. Numerical results corroborate the possibilities and give an impressive prospect of the applications of Monte Carlo methods.
Book Synopsis Explorations in Monte Carlo Methods by : Ronald W. Shonkwiler
Download or read book Explorations in Monte Carlo Methods written by Ronald W. Shonkwiler and published by Springer Science & Business Media. This book was released on 2009-08-11 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems. Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. Each chapter ends with a large collection of problems illustrating and directing the material. This book is suitable as a textbook for students of engineering and the sciences, as well as mathematics.
Book Synopsis The Monte Carlo Method in Condensed Matter Physics by : Kurt Binder
Download or read book The Monte Carlo Method in Condensed Matter Physics written by Kurt Binder and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Monte Carlo method is now widely used and commonly accepted as an important and useful tool in solid state physics and related fields. It is broadly recognized that the technique of "computer simulation" is complementary to both analytical theory and experiment, and can significantly contribute to ad vancing the understanding of various scientific problems. Widespread applications of the Monte Carlo method to various fields of the statistical mechanics of condensed matter physics have already been reviewed in two previously published books, namely Monte Carlo Methods in Statistical Physics (Topics Curro Phys. , Vol. 7, 1st edn. 1979, 2ndedn. 1986) and Applications of the Monte Carlo Method in Statistical Physics (Topics Curro Phys. , Vol. 36, 1st edn. 1984, 2nd edn. 1987). Meanwhile the field has continued its rapid growth and expansion, and applications to new fields have appeared that were not treated at all in the above two books (e. g. studies of irreversible growth phenomena, cellular automata, interfaces, and quantum problems on lattices). Also, new methodic aspects have emerged, such as aspects of efficient use of vector com puters or parallel computers, more efficient analysis of simulated systems con figurations, and methods to reduce critical slowing down at i>hase transitions. Taken together with the extensive activity in certain traditional areas of research (simulation of classical and quantum fluids, of macromolecular materials, of spin glasses and quadrupolar glasses, etc.
Book Synopsis Random Number Generation and Monte Carlo Methods by : James E. Gentle
Download or read book Random Number Generation and Monte Carlo Methods written by James E. Gentle and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo simulation has become one of the most important tools in all fields of science. This book surveys the basic techniques and principles of the subject, as well as general techniques useful in more complicated models and in novel settings. The emphasis throughout is on practical methods that work well in current computing environments.
Book Synopsis Monte Carlo Simulation by : Christopher Z. Mooney
Download or read book Monte Carlo Simulation written by Christopher Z. Mooney and published by SAGE. This book was released on 1997-04-07 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at researchers across the social sciences, this book explains the logic behind the Monte Carlo simulation method and demonstrates its uses for social and behavioural research.
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.
Download or read book Monte Carlo written by George Fishman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: Apart from a thorough exploration of all the important concepts, this volume includes over 75 algorithms, ready for putting into practice. The book also contains numerous hands-on implementations of selected algorithms to demonstrate applications in realistic settings. Readers are assumed to have a sound understanding of calculus, introductory matrix analysis, and intermediate statistics, but otherwise the book is self-contained. Suitable for graduates and undergraduates in mathematics and engineering, in particular operations research, statistics, and computer science.
Book Synopsis Monte Carlo Simulation in Statistical Physics by : Kurt Binder
Download or read book Monte Carlo Simulation in Statistical Physics written by Kurt Binder and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: When learning very formal material one comes to a stage where one thinks one has understood the material. Confronted with a "realiife" problem, the passivity of this understanding sometimes becomes painfully elear. To be able to solve the problem, ideas, methods, etc. need to be ready at hand. They must be mastered (become active knowledge) in order to employ them successfully. Starting from this idea, the leitmotif, or aim, of this book has been to elose this gap as much as possible. How can this be done? The material presented here was born out of a series of lectures at the Summer School held at Figueira da Foz (Portugal) in 1987. The series of lectures was split into two concurrent parts. In one part the "formal material" was presented. Since the background of those attending varied widely, the presentation of the formal material was kept as pedagogic as possible. In the formal part the general ideas behind the Monte Carlo method were developed. The Monte Carlo method has now found widespread appli cation in many branches of science such as physics, chemistry, and biology. Because of this, the scope of the lectures had to be narrowed down. We could not give a complete account and restricted the treatment to the ap plication of the Monte Carlo method to the physics of phase transitions. Here particular emphasis is placed on finite-size effects.
Book Synopsis Monte-Carlo Simulation-Based Statistical Modeling by : Ding-Geng (Din) Chen
Download or read book Monte-Carlo Simulation-Based Statistical Modeling written by Ding-Geng (Din) Chen and published by Springer. This book was released on 2017-02-01 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together expert researchers engaged in Monte-Carlo simulation-based statistical modeling, offering them a forum to present and discuss recent issues in methodological development as well as public health applications. It is divided into three parts, with the first providing an overview of Monte-Carlo techniques, the second focusing on missing data Monte-Carlo methods, and the third addressing Bayesian and general statistical modeling using Monte-Carlo simulations. The data and computer programs used here will also be made publicly available, allowing readers to replicate the model development and data analysis presented in each chapter, and to readily apply them in their own research. Featuring highly topical content, the book has the potential to impact model development and data analyses across a wide spectrum of fields, and to spark further research in this direction.
