Handbook of Monte Carlo Methods

, by Kroese, Dirk P.; Taimre, Thomas; Botev, Zdravko I.

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ISBN: 9780470177938 | 0470177934
Cover: Hardcover
Copyright: 3/15/2011

Handbook of Monte Carlo Methods > ISBN13: 9780470177938

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The purpose of this handbook is to provide an accessible and comprehensive compendium of Monte Carlo techniques and related topics. It contains a mix of theory (summarized), algorithms (pseudo and actual), and applications. Since the audience is broad, the theory is kept to a minimum, this without sacrificing rigor. The book is intended to be used as an essential guide to Monte Carlo methods to quickly look up ideas, procedures, formulas, pictures, etc., rather than purely a monograph for researchers or a textbook for students. As the popularity of these methods continues to grow, and new methods are developed in rapid succession, the staggering number of related techniques, ideas, concepts and algorithms makes it difficult to maintain an overall picture of the Monte Carlo approach. This book attempts to encapsulate the emerging dynamics of this field of study.

Dirk P. Kroese, PhD, is Australian Professorial Fellow in Statistics at The University of Queensland (Australia). Dr. Kroese has more than seventy publications in such areas as stochastic modeling, randomized algorithms, computational statistics, and reliability. He is a pioneer of the cross-entropy method and the coauthor of Simulation and the Monte Carlo Method, Second Edition (Wiley).

Thomas Taimre, PhD, is a Postdoctoral Research Fellow at The University of Queensland. He currently focuses his research on Monte Carlo methods and simulation, from the theoretical foundations to performing computer implementations.

Zdravko I. Botev, PhD, is a Postdoctoral Research Fellow at the University of Montreal (Canada). His research interests include the splitting method for rare-event simulation and kernel density estimation. He is the author of one of the most widely used free MATLAB® statistical software programs for nonparametric kernel density estimation.

Preface
Acknowledgments
Uniform Random Number Generation
Random Numbers
Generators Based on Linear Recurrences
Combined Generators
Other Gnerators
Tests for Random Number Generators
References
Quasirandom Number Generation
Multidimensional Integration
Van der Corput and Digital Sequences
Halton Sequences
Faure Sequences
SobolâÇÖ Sequences
Lattice Methods
Randomization and Scrambling
References
Random Variable Generation
Generic Algorithms Based on Common Transformations
Copulas
Generation Methods for Various Random Objects
References
Probability Distributions
Discrete Distributions
Continuous Distribution
Multivariate Distribution
References
Random Process Generation
Gaussian Processes
Markov Chains
Markov Jump Processes
Poisson Processes
Wiener Process and Brownian Motion
Stochastic Di—erential Equations and Di—usion Processes
Brownian Bridge
Geometric Brownian Motion
Ornstein{Uhlenbeck Process
Reected Brownian Motion
Fractional Brownian Motion
Random Fields
L—evy Processes
Time Series
References
Markov Chain Monte Carlo
Metropolis{Hastings Algorithm
Gibbs Sampler
Specialized Samplers
Implementation Issues
Perfect Sampling
References
Discrete Event Simulation
Simulation Models
Discrete Event Systems
EventâÇôOriented Approach
More Examples of Discrete Event Simulation
References
Statistical Analysis of Simulation Data
Simulation Data
Estimation of Performance Measures for Independent Data
Estimation of SteadyâÇôState Performance Measures
Emprical Cdf
Kernal Density Estimation
Resampling and the Bootstrap Method
Goodness of Fit
References
Variance Reduction
Variance Reduction Example
Antithetic Random Variables
Control Variables
Conditional Monte Carlo
Strati—ed Sampling
Latin Hypercube Sampling
MinimumâÇôVariance Density
Quasi Monte Carlo
References
RareâÇôEvent Simulation
E—ciency Sampling
Importance Sampling Methods for Light Tails
Conditioning Methods for Heavy Tails
StateâÇôDependent Importance Sampling
CrossâÇôEntropy Method for RareâÇôEvent Simulation
Splitting Method
References
Estimation of Derivatives
Gradient Estimation
Finite Di—erence Method
In—nitesimal Perturbation Analysis
Score Function Method
Weak Deriatives
Sensitivity Analysis for Regenerative Processes
References
Randomized Optimization
Stochastic Approximation
Stochastic Counterpart Method
Simulated Annealing
Evolutionary Algorithms
CrossâÇôEntropy Method for Optimization
6 Other Randomized Optimization Techniques
References
CrossâÇôEntropy Method
CrossâÇôEntropy Method
CrossâÇôEntropy Method for Estimation
CrossâÇôEntropy Method for Optimization
References
Particle Methods
Sequential Monte Carlo
Particle Splitting
Splitting for Static RareâÇôEvent Probability Estimaton
Adaptive Splitting Algorithm
Estimation of Multidimensional Integrals
Combinatorial Optimization via Splitting
Markov Chain Monte Carlo With Splitting
References
Applications to Finance
Standard Model
Pricing via Monte Carlo Simulation
Sensitivities
References
Applications to Network Reliability
Network Reliability
Evolution Model for a Static Network
Conditional Monte Carlo
Importance Sampling for Network Reliability
Splitting Method
References
Applications to Di—erential Equations
1 Connections Between Stochastic and Partial Di—erential Equations
Transport Processes and Equations
Connections to ODEs Through Scaling
References
Probability and Stochastic Processes
Elements of Mathematical Statistics
Optimization
Miscellany
References
Acronyms and Abbreviations
List of Symbols
List of Distributions
Index
Table of Contents provided by Publisher. All Rights Reserved.

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Handbook of Monte Carlo Methods

Summary

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Table of Contents

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