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Simulation and the Monte Carlo Method

By Reuven Y. Rubinstein,Dirk P. Kroese
  • ISBN Code: : 1118632389
  • Publisher : John Wiley & Sons
  • Pages : 432
  • Category : Mathematics
  • Reads : 889
  • Book Compatibility : Pdf, ePub, Mobi, Kindle
  • Pdf : simulation-and-the-monte-carlo-method.pdf

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.

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Read Also This Books

Monte Carlo Simulation in Statistical Physics

By Kurt Binder,Dieter W. Heermann
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 3642031633
  • Total of Pages : 202
  • Category : Science
  • Members : 728
  • Pdf File: monte-carlo-simulation-in-statistical-physics.pdf

Book Short Summary:

Monte Carlo Simulation in Statistical Physics deals with the computer simulation of many-body systems in condensed-matter physics and related fields of physics, chemistry and beyond, to traffic flows, stock market fluctuations, etc.). Using random numbers generated by a computer, probability distributions are calculated, allowing the estimation of the thermodynamic properties of various systems. This book describes the theoretical background to several variants of these Monte Carlo methodsand gives a systematic presentation from which newcomers can learn to perform such simulations and to analyze their results. The fifth edition covers Classical as well as Quantum Monte Carlo methods. Furthermore a new chapter on the sampling of free energy landscapes has been added. To help students in their work a special web server has been installed to host programs and discussion groups (http://wwwcp.tphys.uni-heidelberg.de). Prof. Binder was the winner of the Berni J. Alder CECAM Award for Computational Physics 2001 as well as the Boltzmann Medal in 2007.

The Monte Carlo Simulation Method for System Reliability and Risk Analysis

By Enrico Zio
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 1447145887
  • Total of Pages : 198
  • Category : Technology & Engineering
  • Members : 170
  • Pdf File: the-monte-carlo-simulation-method-for-system-reliability-and-risk-analysis.pdf

Book Short Summary:

Monte Carlo simulation is one of the best tools for performing realistic analysis of complex systems as it allows most of the limiting assumptions on system behavior to be relaxed. The Monte Carlo Simulation Method for System Reliability and Risk Analysis comprehensively illustrates the Monte Carlo simulation method and its application to reliability and system engineering. Readers are given a sound understanding of the fundamentals of Monte Carlo sampling and simulation and its application for realistic system modeling. Whilst many of the topics rely on a high-level understanding of calculus, probability and statistics, simple academic examples will be provided in support to the explanation of the theoretical foundations to facilitate comprehension of the subject matter. Case studies will be introduced to provide the practical value of the most advanced techniques. This detailed approach makes The Monte Carlo Simulation Method for System Reliability and Risk Analysis a key reference for senior undergraduate and graduate students as well as researchers and practitioners. It provides a powerful tool for all those involved in system analysis for reliability, maintenance and risk evaluations.

The Monte Carlo Method in Condensed Matter Physics

By Kurt Binder
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 3662028557
  • Total of Pages : 393
  • Category : Science
  • Members : 998
  • Pdf File: the-monte-carlo-method-in-condensed-matter-physics.pdf

Book Short Summary:

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.

Essentials of Monte Carlo Simulation

By Nick T. Thomopoulos
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 1461460220
  • Total of Pages : 174
  • Category : Mathematics
  • Members : 137
  • Pdf File: essentials-of-monte-carlo-simulation.pdf

Book Short Summary:

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.

Monte Carlo Simulation in Statistical Physics

By Kurt Binder,Dieter W. Heermann
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 3662033364
  • Total of Pages : 153
  • Category : Science
  • Members : 391
  • Pdf File: monte-carlo-simulation-in-statistical-physics.pdf

Book Short Summary:

Dealing with the computer simulation of thermodynamic properties of many-body condensed-matter systems that use random numbers generated by a computer, this book describes the theoretical background of several variants of Monte Carlo methods. The result is a systematic course allowing newcomers to perform these simulations for themselves and to analyze their results. This third edition has been updated and expanded by a new chapter on important recent developments in the Monte Carlo methodology.

The Monte Carlo Methods in Atmospheric Optics

By G.I. Marchuk,G.A. Mikhailov,M.A. Nazareliev,R.A. Darbinjan,B.A. Kargin,B.S. Elepov
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer
  • Book Code : 3540352376
  • Total of Pages : 210
  • Category : Science
  • Members : 866
  • Pdf File: the-monte-carlo-methods-in-atmospheric-optics.pdf

Book Short Summary:

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.

Monte Carlo Methods and Models in Finance and Insurance

By Ralf Korn,Elke Korn,Gerald Kroisandt
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : CRC Press
  • Book Code : 9781420076196
  • Total of Pages : 484
  • Category : Mathematics
  • Members : 357
  • Pdf File: monte-carlo-methods-and-models-in-finance-and-insurance.pdf

Book Short Summary:

Offering a unique balance between applications and calculations, Monte Carlo Methods and Models in Finance and Insurance incorporates the application background of finance and insurance with the theory and applications of Monte Carlo methods. It presents recent methods and algorithms, including the multilevel Monte Carlo method, the statistical Romberg method, and the Heath–Platen estimator, as well as recent financial and actuarial models, such as the Cheyette and dynamic mortality models. The authors separately discuss Monte Carlo techniques, stochastic process basics, and the theoretical background and intuition behind financial and actuarial mathematics, before bringing the topics together to apply the Monte Carlo methods to areas of finance and insurance. This allows for the easy identification of standard Monte Carlo tools and for a detailed focus on the main principles of financial and insurance mathematics. The book describes high-level Monte Carlo methods for standard simulation and the simulation of stochastic processes with continuous and discontinuous paths. It also covers a wide selection of popular models in finance and insurance, from Black–Scholes to stochastic volatility to interest rate to dynamic mortality. Through its many numerical and graphical illustrations and simple, insightful examples, this book provides a deep understanding of the scope of Monte Carlo methods and their use in various financial situations. The intuitive presentation encourages readers to implement and further develop the simulation methods.

Monte Carlo Simulation in Statistical Physics

By Kurt Binder,Dieter W. Heermann
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 366230273X
  • Total of Pages : 132
  • Category : Science
  • Members : 710
  • Pdf File: monte-carlo-simulation-in-statistical-physics.pdf

Book Short Summary:

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.

Monte-Carlo Simulation-Based Statistical Modeling

By Ding-Geng (Din) Chen,John Dean Chen
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer
  • Book Code : 9811033072
  • Total of Pages : 430
  • Category : Medical
  • Members : 644
  • Pdf File: monte-carlo-simulation-based-statistical-modeling.pdf

Book Short Summary:

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.

Parametric Estimates by the Monte Carlo Method

By G. A. Mikhailov
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Book Code : 3110941953
  • Total of Pages : 188
  • Category : Mathematics
  • Members : 361
  • Pdf File: parametric-estimates.pdf

Book Short Summary:

This monograph is devoted to the further development of parametric weight Monte Carlo estimates for solving linear and nonlinear integral equations, radiation transfer equations, and boundary value problems, including problems with random parameters. The use of these estimates leads to the construction of new, effective Monte Carlo methods for calculating parametric multiple derivatives of solutions and for the main eigenvalues. The book opens with an introduction on the theory of weight Monte Carlo methods. The following chapters contain new material on solving boundary value problems with complex parameters, mixed problems to parabolic equations, boundary value problems of the second and third kind, and some improved techniques related to vector and nonlinear Helmholtz equations. Special attention is given to the foundation and optimization of the global 'walk on grid' method for solving the Helmholtz difference equation. Additionally, new Monte Carlo methods for solving stochastic radiation transfer problems are presented, including the estimation of probabilistic moments of corresponding critical parameters.

Monte Carlo Methods and Applications

By Ivan Dimov,Karl K. Sabelfeld
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Walter de Gruyter
  • Book Code : 3110293587
  • Total of Pages : 246
  • Category : Mathematics
  • Members : 381
  • Pdf File: monte-carlo-methods-and-applications.pdf

Book Short Summary:

This is the proceedings of the "8th IMACS Seminar on Monte Carlo Methods" held from August 29 to September 2, 2011 in Borovets, Bulgaria, and organized by the Institute of Information and Communication Technologies of the Bulgarian Academy of Sciences in cooperation with the International Association for Mathematics and Computers in Simulation (IMACS). Included are 24 papers which cover all topics presented in the sessions of the seminar: stochastic computation and complexity of high dimensional problems, sensitivity analysis, high-performance computations for Monte Carlo applications, stochastic metaheuristics for optimization problems, sequential Monte Carlo methods for large-scale problems, semiconductor devices and nanostructures.

Monte Carlo Simulation

By Christopher Z. Mooney
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : SAGE Publications
  • Book Code : 1506317901
  • Total of Pages : 112
  • Category : Social Science
  • Members : 697
  • Pdf File: monte-carlo-simulation.pdf

Book Short Summary:

The author explains the logic behind the method and demonstrates its uses for social and behavioral research in: conducting inference using statistics with only weak mathematical theory; testing null hypotheses under a variety of plausible conditions; assessing the robustness of parametric inference to violations of its assumptions; assessing the quality of inferential methods; and comparing the properties of two or more estimators. In addition, Christopher Z Mooney carefully demonstrates how to prepare computer algorithms using GAUSS code and uses several research examples to demonstrate these principles. This volume will enable researchers to execute Monte Carlo Simulation effectively and to interpret the estimated sampling distribution generated from its use.

Monte Carlo Methods in Financial Engineering

By Paul Glasserman
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 0387216170
  • Total of Pages : 596
  • Category : Mathematics
  • Members : 646
  • Pdf File: monte-carlo-methods-in-financial-engineering.pdf

Book Short Summary:

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

Random Number Generation and Monte Carlo Methods

By James E. Gentle
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 147572960X
  • Total of Pages : 247
  • Category : Computers
  • Members : 184
  • Pdf File: random-number-generation-and-monte-carlo-methods.pdf

Book Short Summary:

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.

Random Number Generation and Monte Carlo Methods

By James E. Gentle
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 0387216103
  • Total of Pages : 382
  • Category : Computers
  • Members : 470
  • Pdf File: random-number-generation-and-monte-carlo-methods.pdf

Book Short Summary:

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.

Exploring Monte Carlo Methods

By William L. Dunn,J. Kenneth Shultis
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Elsevier
  • Book Code : 9780080930619
  • Total of Pages : 398
  • Category : Mathematics
  • Members : 399
  • Pdf File: exploring-monte-carlo-methods.pdf

Book Short Summary:

Exploring Monte Carlo Methods is a basic text that describes the numerical methods that have come to be known as "Monte Carlo." The book treats the subject generically through the first eight chapters and, thus, should be of use to anyone who wants to learn to use Monte Carlo. The next two chapters focus on applications in nuclear engineering, which are illustrative of uses in other fields. Five appendices are included, which provide useful information on probability distributions, general-purpose Monte Carlo codes for radiation transport, and other matters. The famous "Buffon’s needle problem" provides a unifying theme as it is repeatedly used to illustrate many features of Monte Carlo methods. This book provides the basic detail necessary to learn how to apply Monte Carlo methods and thus should be useful as a text book for undergraduate or graduate courses in numerical methods. It is written so that interested readers with only an understanding of calculus and differential equations can learn Monte Carlo on their own. Coverage of topics such as variance reduction, pseudo-random number generation, Markov chain Monte Carlo, inverse Monte Carlo, and linear operator equations will make the book useful even to experienced Monte Carlo practitioners. Provides a concise treatment of generic Monte Carlo methods Proofs for each chapter Appendixes include Certain mathematical functions; Bose Einstein functions, Fermi Dirac functions, Watson functions

Monte-Carlo Methods and Stochastic Processes

By Emmanuel Gobet
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  • Publisher : CRC Press
  • Book Code : 1498746233
  • Total of Pages : 310
  • Category : Mathematics
  • Members : 537
  • Pdf File: monte-carlo-methods-and-stochastic-processes.pdf

Book Short Summary:

Developed from the author’s course at the Ecole Polytechnique, Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear focuses on the simulation of stochastic processes in continuous time and their link with partial differential equations (PDEs). It covers linear and nonlinear problems in biology, finance, geophysics, mechanics, chemistry, and other application areas. The text also thoroughly develops the problem of numerical integration and computation of expectation by the Monte-Carlo method. The book begins with a history of Monte-Carlo methods and an overview of three typical Monte-Carlo problems: numerical integration and computation of expectation, simulation of complex distributions, and stochastic optimization. The remainder of the text is organized in three parts of progressive difficulty. The first part presents basic tools for stochastic simulation and analysis of algorithm convergence. The second part describes Monte-Carlo methods for the simulation of stochastic differential equations. The final part discusses the simulation of non-linear dynamics.

Monte Carlo Calculations in Nuclear Medicine, Second Edition

By Michael Ljungberg,Sven-Erik Strand,Michael A. King
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Taylor & Francis
  • Book Code : 1439841101
  • Total of Pages : 357
  • Category : Medical
  • Members : 721
  • Pdf File: monte-carlo-calculations-in-nuclear-medicine-second-edition.pdf

Book Short Summary:

From first principles to current computer applications, Monte Carlo Calculations in Nuclear Medicine, Second Edition: Applications in Diagnostic Imaging covers the applications of Monte Carlo calculations in nuclear medicine and critically reviews them from a diagnostic perspective. Like the first edition, this book explains the Monte Carlo method and the principles behind SPECT and PET imaging, introduces the reader to some Monte Carlo software currently in use, and gives the reader a detailed idea of some possible applications of Monte Carlo in current research in SPECT and PET. New chapters in this edition cover codes and applications in pre-clinical PET and SPECT. The book explains how Monte Carlo methods and software packages can be applied to evaluate scatter in SPECT and PET imaging, collimation, and image deterioration. A guide for researchers and students developing methods to improve image resolution, it also demonstrates how Monte Carlo techniques can be used to simulate complex imaging systems.

Contributions to the Theory of Monte Carlo and Quasi-Monte Carlo Methods

By Giray Okten
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Universal-Publishers
  • Book Code : 1581120419
  • Total of Pages : 108
  • Category : Mathematics
  • Members : 560
  • Pdf File: contributions-to-the-theory-of-monte-carlo-and-quasi-monte-carlo-methods.pdf

Book Short Summary:

Quasi-Monte Carlo methods, which are often described as deterministic versions of Monte Carlo methods, were introduced in the 1950s by number theoreticians. They improve several deficiencies of Monte Carlo methods; such as providing estimates with deterministic bounds and avoiding the paradoxical difficulty of generating random numbers in a computer. However, they have their own drawbacks. First, although they provide faster convergence than Monte Carlo methods asymptotically, the advantage may not be practical to obtain in "high" dimensional problems. Second, there is not a practical way to measure the error of a quasi-Monte Carlo simulation. Finally, unlike Monte Carlo methods, there is a scarcity of error reduction techniques for these methods. In this dissertation, we attempt to provide remedies for the disadvantages of quasi-Monte Carlo methods mentioned above. In the first part of the dissertation, a hybrid-Monte Carlo sequence designed to obtain error reduction in high dimensions is studied. Probabilistic results on the discrepancy of this sequence as well as results obtained by applying the sequence to problems from numerical integration and mathematical finance are presented. In the second part of the dissertation, a new hybrid-Monte Carlo method is introduced, in an attempt to obtain a practical statistical error analysis using low-discrepancy sequences. It is applied to problems from mathematical finance and particle transport theory to compare its effectiveness with the conventional methods. In the last part of the dissertation, a generalized quasi-Monte Carlo integration rule is introduced. A Koksma-Hlawka type inequality for the rule is proved, using a new concept for the variation of a function. As a consequence of the rule, error reduction techniques and in particular an "importance sampling" type statement are derived. Problems from different disciplines are used as practical tests for our methods. The numerical results obtained in favor of the methods suggest the practical advantages that can be realized by their use in a wide variety of applications.

Monte Carlo and Quasi-Monte Carlo Methods 2000

By Kai-Tai Fang,Fred J. Hickernell,Harald Niederreiter
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 3642560466
  • Total of Pages : 548
  • Category : Mathematics
  • Members : 767
  • Pdf File: monte-carlo-and-quasi-monte-carlo-methods-2000.pdf

Book Short Summary:

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.

Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications

By Andreas Kling,Fernando J.C. Barao,Masayuki Nakagawa,Luis Tavora,Pedro Vaz
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 3642182119
  • Total of Pages : 1192
  • Category : Science
  • Members : 688
  • Pdf File: advanced-monte-carlo-for-radiation-physics-particle-transport-simulation-and-applications.pdf

Book Short Summary:

This book focuses on the state of the art of Monte Carlo methods in radiation physics and particle transport simulation and applications. Special attention is paid to algorithm development for modeling, and the analysis of experiments and measurements in a variety of fields.

Monte Carlo and Quasi-Monte Carlo Methods

By Ronald Cools,Dirk Nuyens
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer
  • Book Code : 3319335073
  • Total of Pages : 622
  • Category : Mathematics
  • Members : 437
  • Pdf File: monte-carlo-and-quasi-monte-carlo-methods.pdf

Book Short Summary:

This book presents the refereed proceedings of the Eleventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Leuven (Belgium) in April 2014. 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 very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising, in particular, in finance, statistics and computer graphics.

Monte Carlo Methods

By Malvin H. Kalos,Paula A. Whitlock
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  • Publisher : John Wiley & Sons
  • Book Code : 352761740X
  • Total of Pages : 195
  • Category : Science
  • Members : 504
  • Pdf File: monte-carlo-methods.pdf

Book Short Summary:

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.

Stochastic Simulation and Monte Carlo Methods

By Carl Graham,Denis Talay
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  • Publisher : Springer Science & Business Media
  • Book Code : 3642393632
  • Total of Pages : 260
  • Category : Mathematics
  • Members : 999
  • Pdf File: stochastic-simulation-and-monte-carlo-methods.pdf

Book Short Summary:

In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Itô integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations.

Monte Carlo Methods in Quantum Problems

By M.H. Kalos
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  • Publisher : Springer Science & Business Media
  • Book Code : 940096384X
  • Total of Pages : 291
  • Category : Science
  • Members : 520
  • Pdf File: monte-carlo-methods-in-quantum-problems.pdf

Book Short Summary:

Monte Carlo methods have been a tool of theoretical and computational scientists for many years. In particular, the invention and percolation of the algorithm of Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller sparked a rapid growth of applications to classical statistical mechanics. Although proposals for treatment of quantum systems had been made even earlier, only a few serious calculations had heen carried out. Ruch calculations are generally more consuming of computer resources than for classical systems and no universal algorithm had--or indeed has yet-- emerged. However, with advances in techniques and in sheer computing power, Monte Carlo methods have been used with considerable success in treating quantum fluids and crystals, simple models of nuclear matter, and few-body nuclei. Research at several institutions suggest that they may offer a new approach to quantum chemistry, one that is independent of basis ann yet capable of chemical accuracy. That. Monte Carlo methods can attain the very great precision needed is itself a remarkable achievement. More recently, new interest in such methods has arisen in two new a~as. Particle theorists, in particular K. Wilson, have drawn attention to the rich analogy between quantum field theoty and statistical mechanics and to the merits of Monte Carlo calculations for lattice gauge theories. This has become a rapidly growing sub-field. A related development is associated with lattice problems in quantum physics, particularly with models of solid state systems. The~ is much ferment in the calculation of various one-dimensional problems such as the'Hubbard model.

Monte Carlo Methods

By Adrian Barbu,Song-Chun Zhu
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  • Publisher : Springer Nature
  • Book Code : 9811329710
  • Total of Pages : 422
  • Category : Mathematics
  • Members : 896
  • Pdf File: monte-carlo-methods.pdf

Book Short Summary:

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.

Monte Carlo Device Simulation

By Karl Hess
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  • Publisher : Springer Science & Business Media
  • Book Code : 1461540267
  • Total of Pages : 310
  • Category : Technology & Engineering
  • Members : 156
  • Pdf File: monte-carlo-device-simulation.pdf

Book Short Summary:

Monte Carlo simulation is now a well established method for studying semiconductor devices and is particularly well suited to highlighting physical mechanisms and exploring material properties. Not surprisingly, the more completely the material properties are built into the simulation, up to and including the use of a full band structure, the more powerful is the method. Indeed, it is now becoming increasingly clear that phenomena such as reliabil ity related hot-electron effects in MOSFETs cannot be understood satisfac torily without using full band Monte Carlo. The IBM simulator DAMOCLES, therefore, represents a landmark of great significance. DAMOCLES sums up the total of Monte Carlo device modeling experience of the past, and reaches with its capabilities and opportunities into the distant future. This book, therefore, begins with a description of the IBM simulator. The second chapter gives an advanced introduction to the physical basis for Monte Carlo simulations and an outlook on why complex effects such as collisional broadening and intracollisional field effects can be important and how they can be included in the simulations. References to more basic intro the book. The third chapter ductory material can be found throughout describes a typical relationship of Monte Carlo simulations to experimental data and indicates a major difficulty, the vast number of deformation poten tials required to simulate transport throughout the entire Brillouin zone. The fourth chapter addresses possible further extensions of the Monte Carlo approach and subtleties of the electron-electron interaction.

Monte Carlo Simulation of Semiconductor Devices

By C. Moglestue
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  • Publisher : Springer Science & Business Media
  • Book Code : 9401581339
  • Total of Pages : 334
  • Category : Computers
  • Members : 179
  • Pdf File: monte-carlo-simulation-of-semiconductor-devices.pdf

Book Short Summary:

Particle simulation of semiconductor devices is a rather new field which has started to catch the interest of the world's scientific community. It represents a time-continuous solution of Boltzmann's transport equation, or its quantum mechanical equivalent, and the field equation, without encountering the usual numerical problems associated with the direct solution. The technique is based on first physical principles by following in detail the transport histories of indi vidual particles and gives a profound insight into the physics of semiconductor devices. The method can be applied to devices of any geometrical complexity and material composition. It yields an accurate description of the device, which is not limited by the assumptions made behind the alternative drift diffusion and hydrodynamic models, which represent approximate solutions to the transport equation. While the development of the particle modelling technique has been hampered in the past by the cost of computer time, today this should not be held against using a method which gives a profound physical insight into individual devices and can be used to predict the properties of devices not yet manufactured. Employed in this way it can save the developer much time and large sums of money, both important considerations for the laboratory which wants to keep abreast of the field of device research. Applying it to al ready existing electronic components may lead to novel ideas for their improvement. The Monte Carlo particle simulation technique is applicable to microelectronic components of any arbitrary shape and complexity.

Quantum Monte Carlo

By James B. Anderson
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  • Publisher : Oxford University Press
  • Book Code : 9780199718740
  • Total of Pages : 198
  • Category : Science
  • Members : 303
  • Pdf File: quantum-monte-carlo.pdf

Book Short Summary:

Monte Carlo methods are a class of computational algorithms for simulating the behavior of a wide range of various physical and mathematical systems (with many variables). Their utility has increased with general availability of fast computers, and new applications are continually forthcoming. The basic concepts of Monte Carlo are both simple and straightforward and rooted in statistics and probability theory, their defining characteristic being that the methodology relies on random or pseudo-random sequences of numbers. It is a technique of numerical analysis based on the approximate solution of a problem using repeated sampling experiments and observing the proportion of times a given property is satisfied. The term Monte Carlo was first used to describe calculational methods based on chance in the 1940s, but the methods themselves preceded the term by as much as a century. Quantum Monte Carlo (QMC) first appeared in 1982 and similarly was preceded by development of the related calculational methodology. The success of QMC methods over the past few decades has been remarkable, and this book will clearly demonstrate that success in its discussion of applications. For isolated molecules, the basic material of chemistry, QMC methods have produced exact solutions of the Schroedinger equation for very small systems and the most accurate solutions available for very large systems. The range of applications is impressive: folding of protein molecules, interactions in liquids, structure modeling in crystals and enzymes, quantum dots, designing heat shields and aerodynamic forms, architecture, design, business and economics, and even cinema and video games (3D modeling). This book takes a similar approach to Henry Schaefers classic book Quantum Chemistry (OUP, 1984 now a Dover edition), collecting summaries of some of the most important papers in the quantum Monte Carlo literature, tying everything together with analysis and discussion of applications. Quantum Monte Carlo is a reference book for quantum Monte Carlo applications, belonging near the desk of every quantum chemist, physicist, and a wide range of scientists and engineers across many disciplines, destined to become a classic.

Fast Sequential Monte Carlo Methods for Counting and Optimization

By Reuven Y. Rubinstein,Ad Ridder,Radislav Vaisman
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : John Wiley & Sons
  • Book Code : 1118612353
  • Total of Pages : 208
  • Category : Mathematics
  • Members : 464
  • Pdf File: fast-sequential-monte-carlo-methods-for-counting-and-optimization.pdf

Book Short Summary:

A comprehensive account of the theory and application of Monte Carlo methods Based on years of research in efficient Monte Carlo methods for estimation of rare-event probabilities, counting problems, and combinatorial optimization, Fast Sequential Monte Carlo Methods for Counting and Optimization is a complete illustration of fast sequential Monte Carlo techniques. The book provides an accessible overview of current work in the field of Monte Carlo methods, specifically sequential Monte Carlo techniques, for solving abstract counting and optimization problems. Written by authorities in the field, the book places emphasis on cross-entropy, minimum cross-entropy, splitting, and stochastic enumeration. Focusing on the concepts and application of Monte Carlo techniques, Fast Sequential Monte Carlo Methods for Counting and Optimization includes: Detailed algorithms needed to practice solving real-world problems Numerous examples with Monte Carlo method produced solutions within the 1-2% limit of relative error A new generic sequential importance sampling algorithm alongside extensive numerical results An appendix focused on review material to provide additional background information Fast Sequential Monte Carlo Methods for Counting and Optimization is an excellent resource for engineers, computer scientists, mathematicians, statisticians, and readers interested in efficient simulation techniques. The book is also useful for upper-undergraduate and graduate-level courses on Monte Carlo methods.

Monte Carlo and Quasi-Monte Carlo Methods 2002

By Harald Niederreiter
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  • Publisher : Springer Science & Business Media
  • Book Code : 3642187439
  • Total of Pages : 460
  • Category : Mathematics
  • Members : 659
  • Pdf File: monte-carlo-and-quasi-monte-carlo-methods-2002.pdf

Book Short Summary:

This book represents the refereed proceedings of the Fifth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at the National University of Singapore in the year 2002. An important feature are invited surveys of the state of the art in key areas such as multidimensional numerical integration, low-discrepancy point sets, computational complexity, finance, and other applications of Monte Carlo and quasi-Monte Carlo methods. These proceedings also include 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 area.