Simulation and the Monte Carlo Method

Author: Reuven Y. Rubinstein

Publisher: Wiley-Interscience

ISBN: 9780471089179

Category: Mathematics

Page: 304

View: 7195

This book provides the first simultaneous coverage of the statistical aspects of simulation and Monte Carlo methods, their commonalities and their differences for the solution of a wide spectrum of engineering and scientific problems. It contains standard material usually considered in Monte Carlo simulation as well as new material such as variance reduction techniques, regenerative simulation, and Monte Carlo optimization.

Student Solutions Manual to accompany Simulation and the Monte Carlo Method, Student Solutions Manual

Author: Dirk P. Kroese,Thomas Taimre,Zdravko I. Botev,Reuven Y. Rubinstein

Publisher: John Wiley & Sons

ISBN: 0470285303

Category: Mathematics

Page: 208

View: 971

This accessible new edition explores the major topics in Monte Carlo simulation Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years 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 the transform likelihood ratio method and the screening 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 to rare events estimation and combinatorial optimization Application of Monte Carlo techniques for counting problems, with an emphasis on the parametric minimum cross-entropy method An extensive range of exercises is provided at the end of each chapter, with more difficult sections and exercises marked accordingly for advanced readers. A generous sampling of applied examples is positioned throughout the book, emphasizing various areas of application, and a detailed appendix presents an introduction to exponential families, a discussion of the computational complexity of stochastic programming problems, and sample MATLAB® programs. Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in 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.

Simulation and the Monte Carlo Method, 2nd Edition Set

Author: Reuven Y. Rubinstein

Publisher: Wiley-Interscience

ISBN: 9780470345245

Category: Mathematics

Page: 345

View: 6859

This set contains the text Simulation and the Monte Carlo Method, Second Edition 9780470177945 and the Student Solutions Manual to Accompany Simulation and the Monte Carlo Method, Second Edition 9780470258798.

Handbook of Monte Carlo Methods

Author: Dirk P. Kroese,Thomas Taimre,Zdravko I. Botev

Publisher: John Wiley & Sons

ISBN: 9781118014950

Category: Mathematics

Page: 772

View: 7985

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.

Mechanics and Uncertainty

Author: Maurice Lemaire

Publisher: John Wiley & Sons

ISBN: 111893105X

Category: Technology & Engineering

Page: 176

View: 9432

Science is a quest for certainty, but lack of certainty is the driving force behind all of its endeavors. This book, specifically, examines the uncertainty of technological and industrial science. Uncertainty and Mechanics studies the concepts of mechanical design in an uncertain setting and explains engineering techniques for inventing cost-effective products. Though it references practical applications, this is a book about ideas and potential advances in mechanical science.

Simulation and Monte Carlo

With Applications in Finance and MCMC

Author: J. S. Dagpunar

Publisher: John Wiley & Sons

ISBN: 0470061340

Category: Mathematics

Page: 348

View: 9032

Simulation and Monte Carlo is aimed at students studying for degrees in Mathematics, Statistics, Financial Mathematics, Operational Research, Computer Science, and allied subjects, who wish an up-to-date account of the theory and practice of Simulation. Its distinguishing features are in-depth accounts of the theory of Simulation, including the important topic of variance reduction techniques, together with illustrative applications in Financial Mathematics, Markov chain Monte Carlo, and Discrete Event Simulation. Each chapter contains a good selection of exercises and solutions with an accompanying appendix comprising a Maple worksheet containing simulation procedures. The worksheets can also be downloaded from the web site supporting the book. This encourages readers to adopt a hands-on approach in the effective design of simulation experiments. Arising from a course taught at Edinburgh University over several years, the book will also appeal to practitioners working in the finance industry, statistics and operations research.

Stochastic Simulation

Author: Brian D. Ripley

Publisher: John Wiley & Sons

ISBN: 0470317388

Category: Mathematics

Page: 237

View: 8441

WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. ". . .this is a very competently written and useful addition to the statistical literature; a book every statistician should look at and that many should study!" —Short Book Reviews, International Statistical Institute ". . .reading this book was an enjoyable learning experience. The suggestions and recommendations on the methods [make] this book an excellent reference for anyone interested in simulation. With its compact structure and good coverage of material, it [is] an excellent textbook for a simulation course." —Technometrics ". . .this work is an excellent comprehensive guide to simulation methods, written by a very competent author. It is especially recommended for those users of simulation methods who want more than a 'cook book'. " —Mathematics Abstracts This book is a comprehensive guide to simulation methods with explicit recommendations of methods and algorithms. It covers both the technical aspects of the subject, such as the generation of random numbers, non-uniform random variates and stochastic processes, and the use of simulation. Supported by the relevant mathematical theory, the text contains a great deal of unpublished research material, including coverage of the analysis of shift-register generators, sensitivity analysis of normal variate generators, analysis of simulation output, and more.

An Introduction to Statistical Computing

A Simulation-based Approach

Author: Jochen Voss

Publisher: John Wiley & Sons

ISBN: 1118728025

Category: Mathematics

Page: 400

View: 8282

A comprehensive introduction to sampling-based methods in statistical computing The use of computers in mathematics and statistics has opened up a wide range of techniques for studying otherwise intractable problems. Sampling-based simulation techniques are now an invaluable tool for exploring statistical models. This book gives a comprehensive introduction to the exciting area of sampling-based methods. An Introduction to Statistical Computing introduces the classical topics of random number generation and Monte Carlo methods. It also includes some advanced methods such as the reversible jump Markov chain Monte Carlo algorithm and modern methods such as approximate Bayesian computation and multilevel Monte Carlo techniques An Introduction to Statistical Computing: Fully covers the traditional topics of statistical computing. Discusses both practical aspects and the theoretical background. Includes a chapter about continuous-time models. Illustrates all methods using examples and exercises. Provides answers to the exercises (using the statistical computing environment R); the corresponding source code is available online. Includes an introduction to programming in R. This book is mostly self-contained; the only prerequisites are basic knowledge of probability up to the law of large numbers. Careful presentation and examples make this book accessible to a wide range of students and suitable for self-study or as the basis of a taught course

Stochastic Simulation and Monte Carlo Methods

Mathematical Foundations of Stochastic Simulation

Author: Carl Graham,Denis Talay

Publisher: Springer Science & Business Media

ISBN: 3642393632

Category: Mathematics

Page: 260

View: 8833

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.

Simulation von Schluss-, Minimal- und Maximalwerten spezieller Preisprozesse mit Anwendungen in der Optionsbewertung

Author: Martin Becker

Publisher: BoD – Books on Demand

ISBN: 3837057739


Page: 204

View: 9260

Schluss-, Minimal- und Maximalwerte von Wertpapieren finden sich in Form von Erffnungs-, Hoch-, Tief- und Schlusskursen im Brsenteil nahezu jeder Tages- oder Wochenzeitung. Nicht zuletzt wegen der hervorragenden Verfgbarkeit erfreuen sich diese Kennzahlen, die Informationen der gesamten Preisverlufe aggregieren, groer Beliebtheit. So wird nicht nur die Auszahlung zahlreicher exotischer Optionen vom Hoch-, Tief- und Schlusskurs des betreffenden Underlyings determiniert; Schluss-, Minimal- und Maximalwerte von Preisprozessen werden auch zur Modellschtzung, dabei insbesondere zur Volatilittsschtzung, sowie fr Spezifikationstests eingesetzt. Den Hauptgegenstand dieser Monographie bilden die Entwicklung und Vorstellung effizienter Simulationsverfahren fr Schluss-, Minimal- und Maximalwerte verschiedener populrer zeitstetiger Preisprozesse und die Anpassung dieser Simulationsverfahren fr spezielle Probleme der Monte Carlo-Optionsbewertung. Der Schwerpunkt liegt dabei auf der Entwicklung von Verfahren, die im Gegensatz zu den bekannten, in der Regel auf quidistanten Prozessdiskretisierungen aufbauenden Standardverfahren einen vorgegebenen maximalen Simulationsfehler einhalten und dennoch mit einem deutlich geringeren Bedarf an Rechenzeit (und gegebenenfalls Speicherplatz) auskommen. Ein Kern der Monographie ist die Entwicklung einer Simulationsmethode fr Schluss-, Minimal- und Maximalwerte Brownscher Bewegungen auf der Basis der entsprechenden trivariaten Verteilung, die auf Sprungdiffusionen und weitere Prozesse mit Komponenten Brownscher Bewegungen bertragen wird. Ein zweiter Schwerpunkt liegt auf der Entwicklung einer entsprechenden Simulationsmethode fr Variance Gamma-Prozesse. Die Simulationsverfahren werden schlielich fr das konkrete Problem der Monte Carlo-Bewertung von zeitstetig beobachteten (Double) Barrier Optionen im Black-Scholes-, Merton-Sprungdiffusions- sowie Variance Gamma-Modell angepasst.

Einführung in Statistik und Messwertanalyse für Physiker


Author: G. Bohm,G. Zech

Publisher: N.A

ISBN: 9783540257592


Page: 400

View: 665

Die Einf]hrung in die Statistik und Messwertanalyse f]r Physiker richtet sich weniger an mathematischen \berlegungen aus, sondern stellt die praktische Anwendung in den Vordergrund und schdrft die Intuition experimentelle Ergebnisse richtig einzuschdtzen. Zahlreiche ausf]hrlich betrachtete Beispiele dienen dazu, hdufig bei der Datenanalyse gemachte Fehler zu vermeiden (unsinnige Anwendung des Chi-Quadrattests, Funktionenanpassung bei falscher Parametrisierung, Entfaltung mit willk]rlicher Regularisierung). Ein besonderes Augenmerk wird auf den Vergleich von Daten mit Monte-Carlo-Simulationen gelenkt. Moderne Experimente kommen nicht ohne Simulation aus. Deshalb ist es wichtig zu wissen, wie Parameteranpassungen und Entfaltungen in diesem Fall durchgef]rt werden. Au_erdem werden den Studierenden moderne Entwicklungen der Statistik nahegebracht, die in dlteren Lehrb]chern nicht behandelt werden.

Random processes in physical systems

an introduction to probability-based computer simulations

Author: Charles Allen Whitney

Publisher: Wiley-Interscience


Category: Science

Page: 320

View: 4771

Introduces the reader to applications of computer programs that permit the manipulation of simulated physical systems, unlocking the potential for dramatic insights in the fields of physics, chemistry and statistics. Divided into four sections, it opens with an introduction to pseudo-random numbers and discusses the concept of the ''random walk'' as well as the excitation of atoms whose energy arrives in discrete quanta. Sample listings of computer programs for some of the key calculations are included. Section 2 describes a few of the most important processes that take place in the continuum of time, especially the scattering of photons in a gas and the ''Brownian motion'' of small particles. The third section applies these modeling techniques to the behavior of more complex systems and points the way to what promises to be a major use of computers in the future. Section 4 introduces the application of randomizing methods to the solution of statistical problems such as curve-fitting and error analysis. Using computer methods modeled on the rules of gambling, it promises to be a milestone in the field of physics education.

Fast Sequential Monte Carlo Methods for Counting and Optimization

Author: Reuven Y. Rubinstein,Ad Ridder,Radislav Vaisman

Publisher: John Wiley & Sons

ISBN: 1118612353

Category: Mathematics

Page: 208

View: 1818

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.

Applied Linear Regression

Author: Sanford Weisberg

Publisher: John Wiley & Sons

ISBN: 1118594851

Category: Mathematics

Page: 368

View: 4883

Praise for the Third Edition "...this is an excellent book which could easily be used as acourse text..." —International Statistical Institute The Fourth Edition of Applied LinearRegression provides a thorough update of the basic theoryand methodology of linear regression modeling. Demonstrating thepractical applications of linear regression analysis techniques,the Fourth Edition uses interesting, real-worldexercises and examples. Stressing central concepts such as model building, understandingparameters, assessing fit and reliability, and drawing conclusions,the new edition illustrates how to develop estimation, confidence,and testing procedures primarily through the use of least squaresregression. While maintaining the accessible appeal of eachprevious edition,Applied Linear Regression, FourthEdition features: Graphical methods stressed in the initial exploratory phase,analysis phase, and summarization phase of an analysis In-depth coverage of parameter estimates in both simple andcomplex models, transformations, and regression diagnostics Newly added material on topics including testing, ANOVA, andvariance assumptions Updated methodology, such as bootstrapping, cross-validationbinomial and Poisson regression, and modern model selectionmethods Applied Linear Regression, Fourth Edition is anexcellent textbook for upper-undergraduate and graduate-levelstudents, as well as an appropriate reference guide forpractitioners and applied statisticians in engineering, businessadministration, economics, and the social sciences.

Robust Statistics

The Approach Based on Influence Functions

Author: Frank R. Hampel,Elvezio M. Ronchetti,Peter J. Rousseeuw,Werner A. Stahel

Publisher: John Wiley & Sons

ISBN: 1118150686

Category: Mathematics

Page: 502

View: 2059

The Wiley-Interscience Paperback Series consists of selectedbooks that have been made more accessible to consumers in an effortto increase global appeal and general circulation. With these newunabridged softcover volumes, Wiley hopes to extend the lives ofthese works by making them available to future generations ofstatisticians, mathematicians, and scientists. "This is a nice book containing a wealth of information, much ofit due to the authors. . . . If an instructor designing such acourse wanted a textbook, this book would be the best choiceavailable. . . . There are many stimulating exercises, and the bookalso contains an excellent index and an extensive list ofreferences." —Technometrics "[This] book should be read carefully by anyone who isinterested in dealing with statistical models in a realisticfashion." —American Scientist Introducing concepts, theory, and applications, RobustStatistics is accessible to a broad audience, avoidingallusions to high-powered mathematics while emphasizing ideas,heuristics, and background. The text covers the approach based onthe influence function (the effect of an outlier on an estimater,for example) and related notions such as the breakdown point. Italso treats the change-of-variance function, fundamental conceptsand results in the framework of estimation of a single parameter,and applications to estimation of covariance matrices andregression parameters.

Time Series

Applications to Finance with R and S-Plus

Author: Ngai Hang Chan

Publisher: John Wiley & Sons

ISBN: 1118030710

Category: Mathematics

Page: 330

View: 3551

A new edition of the comprehensive, hands-on guide to financialtime series, now featuring S-Plus® and R software Time Series: Applications to Finance with R and S-Plus®,Second Edition is designed to present an in-depth introduction tothe conceptual underpinnings and modern ideas of time seriesanalysis. Utilizing interesting, real-world applications and thelatest software packages, this book successfully helps readersgrasp the technical and conceptual manner of the topic in order togain a deeper understanding of the ever-changing dynamics of thefinancial world. With balanced coverage of both theory and applications, thisSecond Edition includes new content to accurately reflect thecurrent state-of-the-art nature of financial time series analysis.A new chapter on Markov Chain Monte Carlo presents Bayesian methodsfor time series with coverage of Metropolis-Hastings algorithm,Gibbs sampling, and a case study that explores the relevance ofthese techniques for understanding activity in the Dow JonesIndustrial Average. The author also supplies a new presentation ofstatistical arbitrage that includes discussion of pairs trading andcointegration. In addition to standard topics such as forecastingand spectral analysis, real-world financial examples are used toillustrate recent developments in nonstandard techniques,including: Nonstationarity Heteroscedasticity Multivariate time series State space modeling and stochastic volatility Multivariate GARCH Cointegration and common trends The book's succinct and focused organization allows readers tograsp the important ideas of time series. All examples aresystematically illustrated with S-Plus® and R software,highlighting the relevance of time series in financialapplications. End-of-chapter exercises and selected solutions allowreaders to test their comprehension of the presented material, anda related Web site features additional data sets. Time Series: Applications to Finance with R and S-Plus® isan excellent book for courses on financial time series at theupper-undergraduate and beginning graduate levels. It also servesas an indispensible resource for practitioners working withfinancial data in the fields of statistics, economics, business,and risk management.

Regression Analysis by Example

Author: Samprit Chatterjee,Ali S. Hadi

Publisher: John Wiley & Sons

ISBN: 0470055456

Category: Mathematics

Page: 416

View: 2052

The essentials of regression analysis through practical applications Regression analysis is a conceptually simple method for investigating relationships among variables. Carrying out a successful application of regression analysis, however, requires a balance of theoretical results, empirical rules, and subjective judgement. Regression Analysis by Example, Fourth Edition has been expanded and thoroughly updated to reflect recent advances in the field. The emphasis continues to be on exploratory data analysis rather than statistical theory. The book offers in-depth treatment of regression diagnostics, transformation, multicollinearity, logistic regression, and robust regression. This new edition features the following enhancements: Chapter 12, Logistic Regression, is expanded to reflect the increased use of the logit models in statistical analysis A new chapter entitled Further Topics discusses advanced areas of regression analysis Reorganized, expanded, and upgraded exercises appear at the end of each chapter A fully integrated Web page provides data sets Numerous graphical displays highlight the significance of visual appeal Regression Analysis by Example, Fourth Edition is suitable for anyone with an understanding of elementary statistics. Methods of regression analysis are clearly demonstrated, and examples containing the types of irregularities commonly encountered in the real world are provided. Each example isolates one or two techniques and features detailed discussions of the techniques themselves, the required assumptions, and the evaluated success of each technique. The methods described throughout the book can be carried out with most of the currently available statistical software packages, such as the software package R. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Longitudinal Data Analysis

Author: Donald Hedeker,Robert D. Gibbons

Publisher: John Wiley & Sons

ISBN: 0470036478

Category: Mathematics

Page: 360

View: 5923

Longitudinal data analysis for biomedical and behavioral sciences This innovative book sets forth and describes methods for the analysis of longitudinaldata, emphasizing applications to problems in the biomedical and behavioral sciences. Reflecting the growing importance and use of longitudinal data across many areas of research, the text is designed to help users of statistics better analyze and understand this type of data. Much of the material from the book grew out of a course taught by Dr. Hedeker on longitudinal data analysis. The material is, therefore, thoroughly classroom tested and includes a number of features designed to help readers better understand and apply the material. Statistical procedures featured within the text include: * Repeated measures analysis of variance * Multivariate analysis of variance for repeated measures * Random-effects regression models (RRM) * Covariance-pattern models * Generalized-estimating equations (GEE) models * Generalizations of RRM and GEE for categorical outcomes Practical in their approach, the authors emphasize the applications of the methods, using real-world examples for illustration. Some syntax examples are provided, although the authors do not generally focus on software in this book. Several datasets and computer syntax examples are posted on this title's companion Web site. The authors intend to keep the syntax examples current as new versions of the software programs emerge. This text is designed for both undergraduate and graduate courses in longitudinal data analysis. Instructors can take advantage of overheads and additional course materials available online for adopters. Applied statisticians in biomedicine and the social sciences can also use the book as a convenient reference.