First Course in Monte Carlo

Name: First Course in Monte Carlo
Price: 50.71 USD
Availability: InStock
ISBN: 9780534420468

ISBN-10: 053442046X

ISBN-13: 9780534420468

Edition: 6th 2006

Authors: George Fishman

List price: $269.95

30 day, 100% satisfaction guarantee!

Marketplace

4 new & used from $50.71

what's this?

Rush Rewards U
Members Receive:

You have reached 400 XP and carrot coins. That is the daily max!

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…

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