05204nam 2200613 a 450 991082746820332120200520144314.01-283-17383-297866131738360-08-093061-1(CKB)2670000000074970(EBL)680811(OCoLC)727648959(SSID)ssj0000491979(PQKBManifestationID)12214856(PQKBTitleCode)TC0000491979(PQKBWorkID)10477076(PQKB)10527064(MiAaPQ)EBC680811(PPN)170600521(FR-PaCSA)88811717(EXLCZ)99267000000007497020101228d2012 uy 0engur|n|---|||||txtccrExploring Monte Carlo methods /William L. Dunn, J. Kenneth Shultis1st ed.Amsterdam ;Boston Elsevierc20121 online resource (401 p.)Description based upon print version of record.0-444-51575-5 Includes bibliographical references and index.Front Cover; Exploring Monte Carlo Methods; Copyright; Dedication; Table of Contents; Preface; Chapter 1. Introduction; 1.1 What Is Monte Carlo?; 1.2 A Brief History of Monte Carlo; 1.3 Monte Carlo as Quadrature; 1.4 Monte Carlo as Simulation; 1.5 Preview of Things to Come; 1.6 Summary; Bibliography; Problems; Chapter 2. The Basis of Monte Carlo; 2.1 Single Continuous Random Variables; 2.2 Discrete Random Variables; 2.3 Multiple Random Variables; 2.4 The Law of Large Numbers; 2.5 The Central Limit Theorem; 2.6 Monte Carlo Quadrature; 2.7 Monte Carlo Simulation; 2.8 Summary; BibliographyProblemsChapter 3. Pseudorandom Number Generators; 3.1 Linear Congruential Generators; 3.2 Structure of the Generated Random Numbers; 3.3 Characteristics of Good Random Number Generators; 3.4 Tests for Congruential Generators; 3.5 Practical Multiplicative Congruential Generators; 3.6 Shuffling a Generator's Output; 3.7 Skipping Ahead; 3.8 Combining Generators; 3.9 Other Random Number Generators; 3.10 Summary; Bibliography; Problems; Chapter 4. Sampling, Scoring, and Precision; 4.1 Sampling; 4.2 Scoring; 4.3 Accuracy and Precision; 4.4 Summary; Bibliography; ProblemsChapter 5. Variance Reduction Techniques5.1 Use of Transformations; 5.2 Importance Sampling; 5.3 Systematic Sampling; 5.4 Stratified Sampling; 5.5 Correlated Sampling; 5.6 Partition of the Integration Volume; 5.7 Reduction of Dimensionality; 5.8 Russian Roulette and Splitting; 5.9 Combinations of Different Variance Reduction Techniques; 5.10 Biased Estimators; 5.11 Improved Monte Carlo Integration Schemes; 5.12 Summary; Bibliography; Problems; Chapter 6. Markov Chain Monte Carlo; 6.1 Markov Chains to the Rescue; 6.2 Brief Review of Probability Concepts; 6.3 Bayes Theorem6.4 Inference and Decision Applications6.5 Summary; Bibliography; Problems; Chapter 7. Inverse Monte Carlo; 7.1 Formulation of the Inverse Problem; 7.2 Inverse Monte Carlo by Iteration; 7.3 Symbolic Monte Carlo; 7.4 Inverse Monte Carlo by Simulation; 7.5 General Applications of IMC; 7.6 Summary; Bibliography; Problems; Chapter 8. Linear Operator Equations; 8.1 Linear Algebraic Equations; 8.2 Linear Integral Equations; 8.3 Linear Differential Equations; 8.4 Eigenvalue Problems; 8.5 Summary; Bibliography; Problems; Chapter 9. The Fundamentals of Neutral Particle Transport9.1 Description of the Radiation Field9.2 Radiation Interactions with the Medium; 9.3 Transport Equation; 9.4 Adjoint Transport Equation; 9.5 Summary; Bibliography; Problems; Chapter 10. Monte Carlo Simulation of Neutral Particle Transport; 10.1 Basic Approach for Monte Carlo Transport Simulations; 10.2 Geometry; 10.3 Sources; 10.4 Path-Length Estimation; 10.5 Purely Absorbing Media; 10.6 Type of Collision; 10.7 Time Dependence; 10.8 Particle Weights; 10.9 Scoring and Tallies; 10.10 An Example of One-Speed Particle Transport; 10.11 Monte Carlo Based on the Integral Transport Equation10.12 Variance Reduction and Nonanalog MethodsExploring 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 pMonte Carlo methodMonte Carlo method.518/.282Dunn William L(William Lee),1944-1710844Shultis J. Kenneth627176MiAaPQMiAaPQMiAaPQBOOK9910827468203321Exploring Monte Carlo methods4101759UNINA