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Simulation and the Monte Carlo method (Wiley Series in Probability and Statistics)
Rubinstein R., Kroese D., Wiley-Interscience, 2007. 304 pp. Type: Book
Date Reviewed: Sep 3 2008

This is not an easy book to read. But, if you need to learn how to use Monte Carlo in your simulations, this is probably the best single document I have ever read. Chapter 1 begins with a very broad explanation of basic statistic concepts. After this 46-page introduction, eight chapters follow, discussing all the major issues related to Monte Carlo simulation.

Chapter 2 presents a historical overview of how random numbers are generated, discussing issues related to computer-generated random numbers, including the generation of single numbers, vectors, and Poisson and Markov processes, and ending with the generation of permutations. This chapter presents several algorithms, and thus can be used as a “how to” for novice programmers (although novice programmers may not need to read this book).

Chapter 3 is quite short (only 16 pages). It describes the simulation of discrete events, and presents a good overview of the classification of simulation models. I found it strange that a description of the origin of the “Monte Carlo” is only found on page 82; this could have been included in the introduction. Chapter 4 (also short) presents a very interesting statistical analysis of discrete-event simulation; this includes the analysis of confidence intervals. Chapter 5 presents a very detailed discussion of the theoretical and practical aspects of reducing the variance for simulations on models for which some information is already known.

The problem of simulating Markov chains is described in chapter 6. This is probably the second-best chapter in the book, since the simulation of Markov chains is very common in many scientific fields. Chapter 7 discusses sensitivity analysis in Monte Carlo simulation. It is very well written, and presents several examples on the applicability of sensitivity analysis. The cross-entropy method is actually one of my favorites, and its area of application is extremely broad. The last chapter of the book addresses counting using Monte Carlo--an area that is most often presented in the literature.

An interesting feature of the book is that each chapter is almost self-contained, although sometimes examples refer to previous examples that are in other chapters. Unfortunately, it is sometimes difficult to understand where an example or a theorem ends, since the formatting changes are not clear enough to distinctly mark the end of the subsections. Finally, it would be interesting to see more illustrations; the lack of illustrations is sometimes detrimental to comprehension.

Reviewer:  Nuno M. Garcia Review #: CR136016 (0907-0642)
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Simulation Theory (I.6.1 )
 
 
Monte Carlo (I.6.8 ... )
 
 
Probabilistic Algorithms (Including Monte Carlo) (G.3 ... )
 
 
General (I.6.0 )
 
 
Types Of Simulation (I.6.8 )
 
 
Probability And Statistics (G.3 )
 
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