Apart from a thorough exploration of all the important concepts, this volume includes over 75 algorithms, ready for putting into practice. The book also contains numerous hands-on implementations of selected algorithms to demonstrate applications in realistic settings. Readers are assumed to have a sound understanding of calculus, introductory matrix analysis, and intermediate statistics, but otherwise the book is self-contained. Suitable for graduates and undergraduates in mathematics and engineering, in particular operations research, statistics, and computer science.
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31 of 31 people found the following review helpful:
5.0 out of 5 stars
HIGHLY recommended!!,
By Dr. Lee D. Carlson (Baltimore, Maryland USA) - See all my reviews (VINE VOICE) (HALL OF FAME REVIEWER) (REAL NAME)
This review is from: Monte Carlo (Hardcover)
This book gives a rigorous introduction to the main ideas behind the Monte Carlo technique and also gives many concrete examples to illustrate the important concepts. The applications of Monte Carlo are immense, and cover a wide range of fields, including finance, physics, chemistry, computational biology, geology, computational radiology, and network engineering. The author begins, naturally, with a discussion of how to compute the volume of a high-dimensional body using standard (deterministic) methods and then shows the advantages of using Monte Carlo to find the volume. He does a fine job of assessing the errors in the volume calculation, being careful to distinguish between convergence with probability one and convergence in probability. He also explains the need for specifying confidence levels, and not just the epsilon error term, to determine the smallest sample size that guarantees an error no larger than the specified epsilon. He also gives an interesting application to network reliability in this chapter. The probability that two network nodes are connected is reduced to a volume computation which is then estimated using Monte Carlo sampling. This is an excellent example of how Monte Carlo can be used to arrive at an accurate estimate of an intractable problem. The author gives another example of this later in the chapter wherein he uses Monte Carlo methods in combinatorial probability. Also included in the chapter are some useful hands-on exercises for the reader. The sometimes tricky procedure of generating samples from a variety of distributions is the subject of the next chapter. The author is careful throughout the chapter to distinguish between results that are exact from a formal standpoint and those that are implementable in practice. In addition, a thorough discussion of the error introduced by using pseudorandom numbers in place of sequences of uniform deviates is given. This is the only book I know of that discusses this issue with the clarity it does. The author treats the inverse transform, composition, acceptance-rejection, ratio-of-uniforms, and exact-approximation in great detail. Here again a very useful set of hands-on exercises is given at the end of the chapter. Increasing the efficiency of Monte Carlo sampling is the subject of the next chapter, wherein importance sampling, control variates, stratified sampling, correlated sampling, and conditional Monte Carlo are discussed in detail. These methods are usually called variance reduction techniques, but the author gives an interesting argument about why this characterization is not really accurate. The author brings in conditional sampling, or Markov chain sampling, in the next chapter. It is this approach that has made Monte Carlo such a widely used techniques in science, finance, and network queueing problems. He gives a rather quick overview of the necessary background in Markov chains, and then moves on to discuss neutron transport. It was the intractable nature of the Boltzmann transport equation that gave Monte Carlo its first real application back in the 1940's. The much-used Metropolis method is discussed later, with close attention paid to the details. This is a section that should be read by anyone interested in Monte Carlo techniques. This is followed by a detailed discussion of Markov random fields, Gibbs sampling, and simulated annealing, all of these being heavily used in applications. And also, no book on Monte Carlo could be complete without a discussion of the three-dimensional Ising model, which is in here. The next chapter concentrates on sampling design and statistical inference, wherein the author discusses how choices of the initial (nonequilibrium) distribution, the number of steps, the number of replications, and the simulation time affect the computational and statistical efficiency of the Monte Carlo simulation. He explains very effectively these issues and also the difficulties involved with path-dependence. Network modelers will appreciate his example of routing algorithm performance. The last chapter treats in great detail procedures for generating pseudorandom numbers. The standard methods for doing this are covered, along with spectral tests and performance issues. More exotic pseudorandom generators using nonlinear recursion are also discussed, but the proofs for these are omittted. This excellent book belongs on the shelves of anyone interested in Monte Carlo techniques. The price is reasonable considering how much time it would take to collect all the results in the book from the literature. It deserves a highest recommendation.
11 of 11 people found the following review helpful:
4.0 out of 5 stars
About G.S.Fishman's book,
By "pallavic" (Pavia, Italy) - See all my reviews
This review is from: Monte Carlo (Hardcover)
My work concerns numerical simulations and in particular it deals with monte carlo simulations. I have found this book a good comprehensive reference to explore new numerical methods in a handy way, thanks also for the sketch of many algorithms. However, I wish to prevent anybody who thinks of breaking through these topics starting from this book, since they could be overwhelmed by the huge amount of info.
1 of 3 people found the following review helpful:
3.0 out of 5 stars
Non-Fiction,
By Blue Tyson "- Research Finished" (Legion clubhouse) - See all my reviews
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This review is from: Monte Carlo (Hardcover)
A really high level textbook, this one, you'd have to know some other basics to understand what this book is going on about.
A text only for this with enough mathematical grounding to want to get into this sort of sampling and analysis methodology. Not particularly accessible at all below that.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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cutpoint method, bounded mean computing times, hyperrectangular grid, importance sampling plan, strong stationary time, logarithmic function evaluations, percent normal confidence interval, random coordinate selection, fast acceptance test, sample path data, extant sessions, percent simultaneous confidence intervals, relative error criterion, logarithmic evaluation, relative error criteria, absolute error criterion, asymptotically valid confidence interval, mean stopping time, sample path approach, inverse transform method, approximating confidence interval, normal sample size, single sample path, alias method, feedback shift register generators Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monte Carlo, New York, Department of Computer Science, National Bureau of Standards, Carnegie Mellon University, Department of Mathematics, Generating All Coordinates, Management Science, Modify Algorithm, System Starting, Theory of Computing, Chapel Hill, Department of Operations Research, Englewood Cliffs, Princeton University Press, Stanford University, Test Son, University of North Carolina New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
cutpoint method, bounded mean computing times, hyperrectangular grid, importance sampling plan, strong stationary time, logarithmic function evaluations, percent normal confidence interval, random coordinate selection, fast acceptance test, sample path data, extant sessions, percent simultaneous confidence intervals, relative error criterion, logarithmic evaluation, relative error criteria, absolute error criterion, asymptotically valid confidence interval, mean stopping time, sample path approach, inverse transform method, approximating confidence interval, normal sample size, single sample path, alias method, feedback shift register generators Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monte Carlo, New York, Department of Computer Science, National Bureau of Standards, Carnegie Mellon University, Department of Mathematics, Generating All Coordinates, Management Science, Modify Algorithm, System Starting, Theory of Computing, Chapel Hill, Department of Operations Research, Englewood Cliffs, Princeton University Press, Stanford University, Test Son, University of North Carolina New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 62
books:
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100
books
cite this book:
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- An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition by William Feller in Front Matter, page 143, and page 253
- Applications of Number Theory to Numerical Analysis by S.K. Zaremba in Back Matter (1), and Back Matter (2)
- The Design and Analysis of Computer Algorithms by Alfred V. Aho on page 143, and page 252
- Computer Science: A Concise Introduction by Ian Robertson Sinclair on page 490, and page 491
- Monte Carlo Methods (CRC Monographs on Statistics & Applied Probability) by J. Hammersley on page 333, and page 490
See all 62 books this book cites
- Discrete-Event Simulation by George S. Fishman on 8 pages
- Geschäftsprozesse: Modell- und computergestützte Planung (German Edition) by Friedrich Rosenkranz on 5 pages
- Simulation Methodology for Statisticians, Operations Analysts, and Engineers. Vol. 1 by P. W. A. Lewis in Front Matter, page 97, and page 405
- Simulation with Visual SLAM and AweSim by A. Alan B. Pritsker on page 428, page 443, and page 487
- Value at Risk: Theory and Practice by Glyn A. Holton on page 215, page 224, and Back Matter
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