Exploring Monte Carlo methods

• Main Authors: Dunn, William L. (William Lee), Shultis, J. Kenneth
• Format: eBook Book
• Language: English
• Published: Amsterdam ; Tokyo Academic Press 2012; Elsevier Science & Technology
• Edition: 1
• Subjects: Monte Carlo method

Table of Contents:

• D.4 MCNP and MCNPX -- D.5 MCSHAPE -- D.6 PENELOPE -- D.7 SCALE -- D.8 SRIM -- D.9 TRIPOLI -- Bibliography -- Appendix E: Minimal Standard Pseudorandom Number Generator -- E.1 FORTRAN77 -- E.2 FORTRAN90 -- E.3 Pascal -- E.4 C and C++ -- E.5 Programming Considerations -- Bibliography -- 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 -- Bibliography -- Problems -- Chapter 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 -- Chapter 5. Variance Reduction Techniques -- 5.1 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
• 6.4 Inference and Decision Applications -- 6.5 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 -- 9.1 Description of the Radiation Field -- 9.2 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 -- 10.12 Variance Reduction and Nonanalog Methods -- 10.13 Summary -- Bibliography -- Problems -- Appendix A: Some Common Probability Distributions -- A.1 Continuous Distributions -- A.2 Discrete Distributions -- A.3 Joint Distributions -- Bibliography -- Appendix B: The Weak and Strong Laws of Large Numbers -- B.1 The Weak Law of Large Numbers -- B.2 The Strong Law of Large Numbers -- Bibliography -- Appendix C: Central Limit Theorem -- C.1 Moment Generating Functions -- C.2 Central Limit Theorem -- Bibliography -- Appendix D: Some Popular Monte Carlo Codes for Particle Transport -- D.1 COG -- D.2 EGSnrc -- D.3 GEANT4