Simulation and the Monte Carlo method
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...
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| Main Authors | , |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
Hoboken, N.J
Wiley
2016
John Wiley & Sons, Incorporated Wiley-Blackwell |
| Edition | 3rd ed |
| Series | Wiley series in probability and statistics |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9781118632161 1118632168 1118632206 9781118632208 |
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Table of Contents:
- Intro -- SIMULATION AND THE MONTE CARLO METHOD -- CONTENTS -- PREFACE -- ACKNOWLEDGMENTS -- CHAPTER 1 PRELIMINARIES -- 1.1 INTRODUCTION -- 1.2 RANDOM EXPERIMENTS -- 1.3 CONDITIONAL PROBABILITY AND INDEPENDENCE -- 1.4 RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS -- 1.5 SOME IMPORTANT DISTRIBUTIONS -- 1.6 EXPECTATION -- 1.7 JOINT DISTRIBUTIONS -- 1.8 FUNCTIONS OF RANDOM VARIABLES -- 1.8.1 Linear Transformations -- 1.8.2 General Transformations -- 1.9 TRANSFORMS -- 1.10 JOINTLY NORMAL RANDOM VARIABLES -- 1.11 LIMIT THEOREMS -- 1.12 POISSON PROCESSES -- 1.13 MARKOV PROCESSES -- 1.13.1 Markov Chains -- 1.13.2 Classification of States -- 1.13.3 Limiting Behavior -- 1.13.4 Reversibility -- 1.13.5 Markov Jump Processes -- 1.14 GAUSSIAN PROCESSES -- 1.15 INFORMATION -- 1.15.1 Shannon Entropy -- 1.15.2 Kullback-Leibler Cross-Entropy -- 1.15.3 Maximum Likelihood Estimator and Score Function -- 1.15.4 Fisher Information -- 1.16 CONVEX OPTIMIZATION AND DUALITY -- 1.16.1 Lagrangian Method -- 1.16.2 Duality -- PROBLEMS -- REFERENCES -- CHAPTER 2 RANDOM NUMBER, RANDOM VARIABLE, AND STOCHASTIC PROCESS GENERATION -- 2.1 INTRODUCTION -- 2.2 RANDOM NUMBER GENERATION -- 2.2.1 Multiple Recursive Generators -- 2.2.2 Modulo 2 Linear Generators -- 2.3 RANDOM VARIABLE GENERATION -- 2.3.1 Inverse-Transform Method -- 2.3.2 Alias Method -- 2.3.3 Composition Method -- 2.3.4 Acceptance-Rejection Method -- 2.4 GENERATING FROM COMMONLY USED DISTRIBUTIONS -- 2.4.1 Generating Continuous Random Variables -- 2.4.2 Generating Discrete Random Variables -- 2.5 RANDOM VECTOR GENERATION -- 2.5.1 Vector Acceptance-Rejection Method -- 2.5.2 Generating Variables from a Multinormal Distribution -- 2.5.3 Generating Uniform Random Vectors over a Simplex -- 2.5.4 Generating Random Vectors Uniformly Distributed over a Unit Hyperball and Hypersphere
- 6.7 OTHER MARKOV SAMPLERS -- 6.7.1 Slice Sampler -- 6.7.2 Reversible Jump Sampler -- 6.8 SIMULATED ANNEALING -- 6.9 PERFECT SAMPLING -- PROBLEMS -- REFERENCES -- CHAPTER 7 SENSITIVITY ANALYSIS AND MONTE CARLO OPTIMIZATION -- 7.1 INTRODUCTION -- 7.2 SCORE FUNCTION METHOD FOR SENSITIVITY ANALYSIS OF DESS -- 7.3 SIMULATION-BASED OPTIMIZATION OF DESS -- 7.3.1 Stochastic Approximation -- 7.3.2 Stochastic Counterpart Method -- 7.4 SENSITIVITY ANALYSIS OF DEDS -- PROBLEMS -- REFERENCES -- CHAPTER 8 CROSS-ENTROPY METHOD -- 8.1 INTRODUCTION -- 8.2 ESTIMATION OF RARE-EVENT PROBABILITIES -- 8.2.1 Root-Finding Problem -- 8.2.2 Screening Method for Rare Events -- 8.2.3 CE Method Combined with Sampling from the Zero-Variance Distribution -- 8.3 CE METHOD FOR OPTIMIZATION -- 8.4 MAX-CUT PROBLEM -- 8.5 PARTITION PROBLEM -- 8.5.1 Empirical Computational Complexity -- 8.6 TRAVELING SALESMAN PROBLEM -- 8.6.1 Incomplete Graphs -- 8.6.2 Node Placement -- 8.6.3 Case Studies -- 8.7 CONTINUOUS OPTIMIZATION -- 8.8 NOISY OPTIMIZATION -- 8.9 MINXENT METHOD -- PROBLEMS -- REFERENCES -- CHAPTER 9 SPLITTING METHOD -- 9.1 INTRODUCTION -- 9.2 COUNTING SELF-AVOIDING WALKS VIA SPLITTING -- 9.3 SPLITTING WITH A FIXED SPLITTING FACTOR -- 9.4 SPLITTING WITH A FIXED EFFORT -- 9.5 GENERALIZED SPLITTING -- 9.6 ADAPTIVE SPLITTING -- 9.7 APPLICATION OF SPLITTING TO NETWORK RELIABILITY -- 9.8 APPLICATIONS TO COUNTING -- 9.9 CASE STUDIES FOR COUNTING WITH SPLITTING -- 9.9.1 Satisfiability (SAT) Problem -- 9.9.2 Independent Sets -- 9.9.3 Permanent and Counting Perfect Matchings -- 9.9.4 Binary Contingency Tables -- 9.9.5 Vertex Coloring -- 9.10 SPLITTING AS A SAMPLING METHOD -- 9.11 SPLITTING FOR OPTIMIZATION -- 9.11.1 Continuous Optimization -- PROBLEMS -- REFERENCES -- CHAPTER 10 STOCHASTIC ENUMERATION METHOD -- 10.1 INTRODUCTION -- 10.2 TREE SEARCH AND TREE COUNTING
- 2.5.5 Generating Random Vectors Uniformly Distributed inside a Hyperellipsoid -- 2.6 GENERATING POISSON PROCESSES -- 2.7 GENERATING MARKOV CHAINS AND MARKOV JUMP PROCESSES -- 2.7.1 Random Walk on a Graph -- 2.7.2 Generating Markov Jump Processes -- 2.8 GENERATING GAUSSIAN PROCESSES -- 2.9 GENERATING DIFFUSION PROCESSES -- 2.10 GENERATING RANDOM PERMUTATIONS -- PROBLEMS -- REFERENCES -- CHAPTER 3 SIMULATION OF DISCRETE-EVENT SYSTEMS -- 3.1 INTRODUCTION -- 3.2 SIMULATION MODELS -- 3.2.1 Classification of Simulation Models -- 3.3 SIMULATION CLOCK AND EVENT LIST FOR DEDS -- 3.4 DISCRETE-EVENT SIMULATION -- 3.4.1 Tandem Queue -- 3.4.2 Repairman Problem -- PROBLEMS -- REFERENCES -- CHAPTER 4 STATISTICAL ANALYSIS OF DISCRETE-EVENT SYSTEMS -- 4.1 INTRODUCTION -- 4.2 ESTIMATORS AND CONFIDENCE INTERVALS -- 4.3 STATIC SIMULATION MODELS -- 4.4 DYNAMIC SIMULATION MODELS -- 4.4.1 Finite-Horizon Simulation -- 4.4.2 Steady-State Simulation -- 4.5 BOOTSTRAP METHOD -- PROBLEMS -- REFERENCES -- CHAPTER 5 CONTROLLING THE VARIANCE -- 5.1 INTRODUCTION -- 5.2 COMMON AND ANTITHETIC RANDOM VARIABLES -- 5.3 CONTROL VARIABLES -- 5.4 CONDITIONAL MONTE CARLO -- 5.4.1 Variance Reduction for Reliability Models -- 5.5 STRATIFIED SAMPLING -- 5.6 MULTILEVEL MONTE CARLO -- 5.7 IMPORTANCE SAMPLING -- 5.7.1 Weighted Samples -- 5.7.2 Variance Minimization Method -- 5.7.3 Cross-Entropy Method -- 5.8 SEQUENTIAL IMPORTANCE SAMPLING -- 5.9 SEQUENTIAL IMPORTANCE RESAMPLING -- 5.10 NONLINEAR FILTERING FOR HIDDEN MARKOV MODELS -- 5.11 TRANSFORM LIKELIHOOD RATIO METHOD -- 5.12 PREVENTING THE DEGENERACY OF IMPORTANCE SAMPLING -- PROBLEMS -- REFERENCES -- CHAPTER 6 MARKOV CHAIN MONTE CARLO -- 6.1 INTRODUCTION -- 6.2 METROPOLIS-HASTINGS ALGORITHM -- 6.3 HIT-AND-RUN SAMPLER -- 6.4 GIBBS SAMPLER -- 6.5 ISING AND POTTS MODELS -- 6.5.1 Ising Model -- 6.5.2 Potts Model -- 6.6 BAYESIAN STATISTICS
- 10.3 KNUTH'S ALGORITHM FOR ESTIMATING THE COST OF A TREE -- 10.4 STOCHASTIC ENUMERATION -- 10.4.1 Combining SE with Oracles -- 10.5 APPLICATION OF SE TO COUNTING -- 10.5.1 Counting the Number of Paths in a Network -- 10.5.2 Counting SATs -- 10.5.3 Counting the Number of Perfect Matchings in a Bipartite Graph -- 10.6 APPLICATION OF SE TO NETWORK RELIABILITY -- 10.6.1 Numerical Results -- PROBLEMS -- REFERENCES -- APPENDIX -- A.1 CHOLESKY SQUARE ROOT METHOD -- A.2 EXACT SAMPLING FROM A CONDITIONAL BERNOULLI DISTRIBUTION -- A.3 EXPONENTIAL FAMILIES -- A.4 SENSITIVITY ANALYSIS -- A.4.1 Convexity Results -- A.4.2 Monotonicity Results -- A.5 A SIMPLE CE ALGORITHM FOR OPTIMIZING THE PEAKS FUNCTION -- A.6 DISCRETE-TIME KALMAN FILTER -- A.7 BERNOULLI DISRUPTION PROBLEM -- A.8 COMPLEXITY -- A.8.1 Complexity of Rare-Event Algorithms -- A.8.2 Complexity of Randomized Algorithms: FPRAS and FPAUS -- A.8.3 SATs in CNF -- A.8.4 Complexity of Stochastic Programming Problems -- PROBLEMS -- REFERENCES -- ABBREVIATIONS AND ACRONYMS -- LIST OF SYMBOLS -- INDEX -- EULA