LEADER 05204nam 2200613 a 450 001 9910827468203321 005 20200520144314.0 010 $a1-283-17383-2 010 $a9786613173836 010 $a0-08-093061-1 035 $a(CKB)2670000000074970 035 $a(EBL)680811 035 $a(OCoLC)727648959 035 $a(SSID)ssj0000491979 035 $a(PQKBManifestationID)12214856 035 $a(PQKBTitleCode)TC0000491979 035 $a(PQKBWorkID)10477076 035 $a(PQKB)10527064 035 $a(MiAaPQ)EBC680811 035 $a(PPN)170600521 035 $a(FR-PaCSA)88811717 035 $a(EXLCZ)992670000000074970 100 $a20101228d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aExploring Monte Carlo methods /$fWilliam L. Dunn, J. Kenneth Shultis 205 $a1st ed. 210 $aAmsterdam ;$aBoston $cElsevier$dc2012 215 $a1 online resource (401 p.) 300 $aDescription based upon print version of record. 311 $a0-444-51575-5 320 $aIncludes bibliographical references and index. 327 $aFront 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; Bibliography 327 $aProblemsChapter 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; Problems 327 $aChapter 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 Theorem 327 $a6.4 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 Transport 327 $a9.1 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 Equation 327 $a10.12 Variance Reduction and Nonanalog Methods 330 $aExploring 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 p 606 $aMonte Carlo method 615 0$aMonte Carlo method. 676 $a518/.282 700 $aDunn$b William L$g(William Lee),$f1944-$01710844 701 $aShultis$b J. Kenneth$0627176 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827468203321 996 $aExploring Monte Carlo methods$94101759 997 $aUNINA