Simulation and the Monte Carlo Method by Rubinstein, Reuven Y. -- Read -- Imperial Library of Trantor

Index

Cover Title Page Copyright Dedication 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 1.9 Transforms 1.10 Jointly Normal Random Variables 1.11 Limit Theorems 1.12 Poisson Processes 1.13 Markov Processes 1.14 Gaussian Processes 1.15 Information 1.16 Convex Optimization and Duality

Chapter 2 Random Number, Random Variable, and Stochastic Process Generation

2.1 Introduction 2.2 Random Number Generation 2.3 Random Variable Generation 2.4 Generating from Commonly Used Distributions 2.5 Random Vector Generation 2.6 Generating Poisson Processes 2.7 Generating Markov Chains and Markov Jump Processes 2.8 Generating Gaussian Processes 2.9 Generating Diffusion Processes 2.10 Generating Random Permutations

Chapter 3 Simulation of Discrete-Event Systems

3.1 Introduction 3.2 Simulation Models 3.3 Simulation Clock and Event List for DEDS 3.4 Discrete-Event Simulation

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 4.5 Bootstrap Method

Chapter 5 Controlling the Variance

5.1 Introduction 5.2 Common and Antithetic Random Variables 5.3 Control Variables 5.4 Conditional Monte Carlo 5.5 Stratified Sampling 5.6 Multilevel Monte Carlo 5.7 Importance Sampling 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

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 6.6 Bayesian Statistics 6.7 Other Markov Samplers 6.8 Simulated Annealing 6.9 Perfect Sampling

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 7.4 Sensitivity Analysis of DEDS

Chapter 8 Cross-Entropy Method

8.1 Introduction 8.2 Estimation of Rare-Event Probabilities 8.3 CE Method for Optimization 8.4 Max-Cut Problem 8.5 Partition Problem 8.6 Traveling Salesman Problem 8.7 Continuous Optimization 8.8 Noisy Optimization 8.9 MinxEnt Method

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 9.10 Splitting as a Sampling Method 9.11 Splitting for Optimization

Chapter 10 Stochastic Enumeration Method

10.1 Introduction 10.2 Tree Search and Tree Counting 10.3 Knuth’s Algorithm for Estimating the Cost of a Tree 10.4 Stochastic Enumeration 10.5 Application of SE to Counting 10.6 Application of SE to Network Reliability

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.5 A Simple CE Algorithm for Optimizing the Peaks Function A.6 Discrete-Time Kalman Filter A.7 Bernoulli Disruption Problem A.8 Complexity

Abbreviations and Acronyms List of Symbols Index Eula