Probability Simulations
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Probability Simulations
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Author : Mary Jean Winter
language : en
Publisher:
Release Date : 2000
Probability Simulations written by Mary Jean Winter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Calculators categories.
Introduction To Probability Simulation And Gibbs Sampling With R
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Author : Eric A. Suess
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-15
Introduction To Probability Simulation And Gibbs Sampling With R written by Eric A. Suess and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-15 with Mathematics categories.
The first seven chapters use R for probability simulation and computation, including random number generation, numerical and Monte Carlo integration, and finding limiting distributions of Markov Chains with both discrete and continuous states. Applications include coverage probabilities of binomial confidence intervals, estimation of disease prevalence from screening tests, parallel redundancy for improved reliability of systems, and various kinds of genetic modeling. These initial chapters can be used for a non-Bayesian course in the simulation of applied probability models and Markov Chains. Chapters 8 through 10 give a brief introduction to Bayesian estimation and illustrate the use of Gibbs samplers to find posterior distributions and interval estimates, including some examples in which traditional methods do not give satisfactory results. WinBUGS software is introduced with a detailed explanation of its interface and examples of its use for Gibbs sampling for Bayesian estimation. No previous experience using R is required. An appendix introduces R, and complete R code is included for almost all computational examples and problems (along with comments and explanations). Noteworthy features of the book are its intuitive approach, presenting ideas with examples from biostatistics, reliability, and other fields; its large number of figures; and its extraordinarily large number of problems (about a third of the pages), ranging from simple drill to presentation of additional topics. Hints and answers are provided for many of the problems. These features make the book ideal for students of statistics at the senior undergraduate and at the beginning graduate levels.
Probability And Simulation
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Author : Giray Ökten
language : en
Publisher: Springer Nature
Release Date : 2020-10-15
Probability And Simulation written by Giray Ökten and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-15 with Mathematics categories.
This undergraduate textbook presents an inquiry-based learning course in stochastic models and computing designed to serve as a first course in probability. Its modular structure complements a traditional lecture format, introducing new topics chapter by chapter with accompanying projects for group collaboration. The text addresses probability axioms leading to Bayes’ theorem, discrete and continuous random variables, Markov chains, and Brownian motion, as well as applications including randomized algorithms, randomized surveys, Benford’s law, and Monte Carlo methods. Adopting a unique application-driven approach to better study probability in action, the book emphasizes data, simulation, and games to strengthen reader insight and intuition while proving theorems. Additionally, the text incorporates codes and exercises in the Julia programming language to further promote a hands-on focus in modelling. Students should have prior knowledge of single variable calculus. Giray Ökten received his PhD from Claremont Graduate University. He has held academic positions at University of Alaska Fairbanks, Ball State University, and Florida State University. He received a Fulbright U.S. Scholar award in 2015. He is the author of an open access textbook in numerical analysis, First Semester in Numerical Analysis with Julia, published by Florida State University Libraries, and a co-author of a children’s math book, The Mathematical Investigations of Dr. O and Arya, published by Tumblehome. His research interests include Monte Carlo methods and computational finance.
Computational Probability And Simulation
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Author : Sidney J. Yakowitz
language : en
Publisher: Addison Wesley Publishing Company
Release Date : 1977
Computational Probability And Simulation written by Sidney J. Yakowitz and has been published by Addison Wesley Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Computers categories.
Random processes and Random number generators; Simulation of probability experiments; Gaming, Random Walks, and linear equations; Gambler's ruin with extensions to inventory control; Limiting processes for Random Walks and time series simulation; Monte Carlo integration and solution of differential equations.
Introduction To Rare Event Simulation
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Author : James Bucklew
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Introduction To Rare Event Simulation written by James Bucklew and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This book presents a unified theory of rare event simulation and the variance reduction technique known as importance sampling from the point of view of the probabilistic theory of large deviations. It allows us to view a vast assortment of simulation problems from a unified single perspective.
Stochastic Simulation And Monte Carlo Methods
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Author : Carl Graham
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-16
Stochastic Simulation And Monte Carlo Methods written by Carl Graham and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-16 with Mathematics categories.
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 And The Monte Carlo Method
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Author : Reuven Y. Rubinstein
language : en
Publisher: John Wiley & Sons
Release Date : 2009-09-25
Simulation And The Monte Carlo Method written by Reuven Y. Rubinstein and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-25 with Mathematics categories.
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.
Simulation And The Monte Carlo Method
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Author : Reuven Y. Rubinstein
language : en
Publisher: John Wiley & Sons
Release Date : 2016-10-20
Simulation And The Monte Carlo Method written by Reuven Y. Rubinstein and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-20 with Mathematics categories.
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.
Probability Theory Problems Simulations
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Author : Hannelore Lisei
language : en
Publisher: World Scientific Publishing Company
Release Date : 2020-02-13
Probability Theory Problems Simulations written by Hannelore Lisei and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-13 with Mathematics categories.
A key pedagogical feature of the textbook is the accessible approach to probability concepts through examples with explanations and problems with solutions. The reader is encouraged to simulate in Matlab random experiments and to explore the theoretical aspects of the probabilistic models behind the studied experiments. By this appropriate balance between simulations and rigorous mathematical approach, the reader can experience the excitement of comprehending basic concepts and can develop the intuitive thinking in solving problems. The current textbook does not contain proofs for the stated theorems, but corresponding references are given. Moreover, the given Matlab codes and detailed solutions make the textbook accessible to researchers and undergraduate students, by learning various techniques from probability theory and its applications in other fields. This book is intended not only for students of mathematics but also for students of natural sciences, engineering, computer science and for science researchers, who possess the basic knowledge of calculus for the mathematical concepts of the textbook and elementary programming skills for the Matlab simulations.
Lectures On Contemporary Probability
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Author : Gregory F. Lawler
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Lectures On Contemporary Probability written by Gregory F. Lawler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This volume is based on classes in probability for advanced undergraduates held at the IAS/Park City Mathematics Institute. It is derived from both lectures (Chapters 1-10) and computer simulations (Chapters 11-13) that were held during the program. The material is coordinated so that some of the major computer simulations relate to topics covered in the first ten chapters. The goal is to present topics that are accessible to advanced undergraduates, yet are areas of current research in probability. The combination of the lucid yet informal style of the lectures and the hands-on nature of the simulations allows readers to become familiar with some interesting and active areas of probability. The first four chapters discuss random walks and the continuous limit of random walks: Brownian motion. Chapters 5 and 6 consider the fascinating mathematics of card shuffles, including the notions of random walks on a symmetric group and the general idea of random permutations. Chapters 7 and 8 discuss Markov chains, beginning with a standard introduction to the theory. Chapter 8 addresses the recent important application of Markov chains to simulations of random systems on large finite sets: Markov Chain Monte Carlo. Random walks and electrical networks are covered in Chapter 9. Uniform spanning trees, as connected to probability and random walks, are treated in Chapter 10. The final three chapters of the book present simulations. Chapter 11 discusses simulations for random walks. Chapter 12 covers simulation topics such as sampling from continuous distributions, random permutations, and estimating the number of matrices with certain conditions using Markov Chain Monte Carlo. Chapter 13 presents simulations of stochastic differential equations for applications in finance. (The simulations do not require one particular piece of software. They can be done in symbolic computation packages or via programming languages such as $\bold C$.) The volume concludes with a number of problems ranging from routine to very difficult. Of particular note are the problems that are typical of simulation problems given to students by the authors when teaching undergraduate probability.