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First Course in Monte Carlo

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ISBN-10: 053442046X

ISBN-13: 9780534420468

Edition: 6th 2006

Authors: George Fishman

List price: $269.95
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A COURSE IN MONTE CARLO is a concise explanation of the Monte Carlo (MC) method. In addition to providing guidance for generating samples from diverse distributions, it describes how to design, perform, and analyze the results of MC experiments based on independent replications, Markov chain MC, and MC optimization. The text gives considerable emphasis to the variance-reducing techniques of importance sampling, stratified sampling, Rao-Blackwellization, control variates, antithetic variates, and quasi-random numbers. For solving optimization problems it describes several MC techniques, including simulated annealing, simulated tempering, swapping, stochastic tunneling, and genetic…    
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Book details

List price: $269.95
Edition: 6th
Copyright year: 2006
Publisher: Brooks/Cole
Publication date: 10/5/2005
Binding: Hardcover
Pages: 350
Size: 7.75" wide x 9.75" long x 1.00" tall
Weight: 1.848
Language: English

George Fishman has regularly contributed to the literature on the Monte Carlo method and discrete-event simulation over the last 40 years. His earlier book, MONTE CARLO: CONCEPTS, ALGORITHMS, AND APPLICATIONS (Springer-Verlag, 1996) won the 1996 Lancaster award for best publication of the Institute for Operations Research and Management Sciences (INFORMS) and the 1997 outstanding publication award of the INFORMS College on Simulation.

Introduction
About this Book
Integration and Summation
Improving Efficiency
Minimizing a Function
Improving Efficiency
Reading Plans
Exercises
Software
Notations
References
Independent Monte Carlo
Independent Monte Carlo (IMC)
Why Monte Carlo?
Generating Samples
Choosing a Monte Carlo Sampling Plan
Importance Sampling
Estimating Volume
Interpreting Relative Error
Product and Non-Product Spaces
Bootstrap Method
Regression Analysis
Lessons Learned
Hands-On Exercises
References
Sampling Generation
Selecting a Sampling Algorithm
Independent and Dependent Variates
Inverse-Transform Method
Restricted Sampling
Discrete Distributions
Sampling from a Table
Restricted Sampling
Composition Method
Acceptance-Rejection Method
Squeeze Method
Adaptive Method
Ratio-of-Uniforms Method
Lessons Learned
Exercises
References
Pseudorandom Number Generation
Linear Congruential Generators
Prime Modulus
Evaluating PNG's
Theoretical Evaluation
Empirical Testing
Collision Test
Birthday Spacings Test
LCG's with Modulus 2(Beta).M = 2(superscript)32.M = 2(superscript)48
Mixed Linear Congruential Generators
Combined Generators
AWC and SWB Generators
Twisted GFSR Generators
Mersenne Twisted GFSRs
Lessons Learned
References
Variance Reduction
Stratified Sampling
Unequal Sample Sizes
Rao-Blackwellization
Exceedance Probabilities for Rare Events
Control Variates
Antithetic Variates
Quasirandom Numbers
Exercises
Lessons Learned
Hands-On Exercises
References
Markov Chain Monte Carlo
Hastings-Metropolis Method
Reversibility
Coordinate Updating
Single-Coordinate Updating
Bayesian MCMC
Joint and Full Conditional Distributions
Gibbs Sampling
Convergence for Xj
Non-connected State Spaces and Mixtures
Convergence for (Lambda)t
Local and Global Moves
Problem Size
Variance of Estimate
Choosing a Nominating Kernel
Independence Hastings-Metropolis Sampling
Random-Walk Nominating Kernels
Chains Favoring Smaller (Sigma)(infinity)squared
General-State Spaces
Polynomial Convergence
Discrete-Event Systems
First-Passage Times
Absorbing States
Lessons Learned
Appendix: Modified Acceptance-Rejection Sampling
Appendix: Modified Acceptance-Rejection Sampling
Exercises
Hands-On Exercises
References
MCMC Sample-Path Analysis
Multiple Independent Replications
Single Sample Path
Estimating the Warm-Up Interval
Batch-Means Method
FNB Rule
SQRT Rule
ABATCH Rule
Testing for Independence
Appendix: LABATCH.2
Lessons Learned
Hands-On Exercises
References
Optimization Via Mcmc
Searching for the Global Optimum
Nominating Kernels
Cooling
Initial Temperature
Temperature Gradient
Stage Length
Stopping Rule
Local Minima
Accelerating Convergence
Simulated Tempering
Swapping
Stochastic Tunneling
Genetic Algorithms
Searching for More Than the Minimum
Lessons Learned
Hands-On Exercises
References
Advanced Concepts In Mcmc
Exploiting Reversibility
Rapid Mixing
Markov Random Fields
Gibbs Distribution
Potts Model
Random Cluster Model
Problem Size
More General Models
Slice Sampling
Product Slice Sampling
Partial Decoupling
Coupling from the Past
Monotone Markov Chains
Reusing Randomness
Total Number of Steps
Saving Space
Independent Hastings-Metropolis Sampling
Lessons Learned
Exercises
References