Monte Carlo Methods for Applied Scientists
Monte Carlo Methods for Applied Scientists

Author: Ivan Dimov

Publisher: World Scientific

Published: 2008

Total Pages: 308

ISBN-13: 9812779892

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The Monte Carlo method is inherently parallel and the extensive and rapid development in parallel computers, computational clusters and grids has resulted in renewed and increasing interest in this method. At the same time there has been an expansion in the application areas and the method is now widely used in many important areas of science including nuclear and semiconductor physics, statistical mechanics and heat and mass transfer. This book attempts to bridge the gap between theory and practice concentrating on modern algorithmic implementation on parallel architecture machines. Although a suitable text for final year postgraduate mathematicians and computational scientists it is principally aimed at the applied scientists: only a small amount of mathematical knowledge is assumed and theorem proving is kept to a minimum, with the main focus being on parallel algorithms development often to applied industrial problems. A selection of algorithms developed both for serial and parallel machines are provided. Sample Chapter(s). Chapter 1: Introduction (231 KB). Contents: Basic Results of Monte Carlo Integration; Optimal Monte Carlo Method for Multidimensional Integrals of Smooth Functions; Iterative Monte Carlo Methods for Linear Equations; Markov Chain Monte Carlo Methods for Eigenvalue Problems; Monte Carlo Methods for Boundary-Value Problems (BVP); Superconvergent Monte Carlo for Density Function Simulation by B-Splines; Solving Non-Linear Equations; Algorithmic Effciency for Different Computer Models; Applications for Transport Modeling in Semiconductors and Nanowires. Readership: Applied scientists and mathematicians.

Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing

Author: Jun S. Liu

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 350

ISBN-13: 0387763716

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This book provides a self-contained and up-to-date treatment of the Monte Carlo method and develops a common framework under which various Monte Carlo techniques can be "standardized" and compared. Given the interdisciplinary nature of the topics and a moderate prerequisite for the reader, this book should be of interest to a broad audience of quantitative researchers such as computational biologists, computer scientists, econometricians, engineers, probabilists, and statisticians. It can also be used as a textbook for a graduate-level course on Monte Carlo methods.

Monte Carlo Simulation and Resampling Methods for Social Science
Monte Carlo Simulation and Resampling Methods for Social Science

Author: Thomas M. Carsey

Publisher: SAGE Publications

Published: 2013-08-05

Total Pages: 304

ISBN-13: 1483324923

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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.

Monte Carlo Methods in Financial Engineering
Monte Carlo Methods in Financial Engineering

Author: Paul Glasserman

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 603

ISBN-13: 0387216170

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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

Monte Carlo Methods
Monte Carlo Methods

Author: Adrian Barbu

Publisher: Springer Nature

Published: 2020-02-24

Total Pages: 433

ISBN-13: 9811329710

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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.

Explorations in Monte Carlo Methods
Explorations in Monte Carlo Methods

Author: Ronald W. Shonkwiler

Publisher: Springer Science & Business Media

Published: 2009-08-11

Total Pages: 249

ISBN-13: 0387878378

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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.

Advanced Markov Chain Monte Carlo Methods
Advanced Markov Chain Monte Carlo Methods

Author: Faming Liang

Publisher: John Wiley & Sons

Published: 2011-07-05

Total Pages: 308

ISBN-13: 1119956803

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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.

Sequential Monte Carlo Methods in Practice
Sequential Monte Carlo Methods in Practice

Author: Arnaud Doucet

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 590

ISBN-13: 1475734379

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Monte Carlo methods are revolutionizing the on-line analysis of data in many fileds. They have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques.

Forecasting in Mathematics
Forecasting in Mathematics

Author: Abdo Abou Jaoude

Publisher: BoD – Books on Demand

Published: 2021-01-27

Total Pages: 156

ISBN-13: 1838808256

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Mathematical probability and statistics are an attractive, thriving, and respectable part of mathematics. Some mathematicians and philosophers of science say they are the gateway to mathematics’ deepest mysteries. Moreover, mathematical statistics denotes an accumulation of mathematical discussions connected with efforts to most efficiently collect and use numerical data subject to random or deterministic variations. Currently, the concept of probability and mathematical statistics has become one of the fundamental notions of modern science and the philosophy of nature. This book is an illustration of the use of mathematics to solve specific problems in engineering, statistics, and science in general.

Handbook of Monte Carlo Methods
Handbook of Monte Carlo Methods

Author: Dirk P. Kroese

Publisher: John Wiley & Sons

Published: 2013-06-06

Total Pages: 627

ISBN-13: 1118014952

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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.