Simulation : A Modeler's Approach (Wiley Series in Probability and Statistics)

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Summary: State of the art on simulation models
Review: I found Thompson's book a pleasure to read. I was amazed to find out that difficult mathematical problems (such as the Gambler's Ruin problem, or Fokker-Planck's model) can be analyzed much easier when a microaxiomatic format with a simulation flow diagram is derived. Thompson uses a very clear style to explain things. Geometric Brownian processes, resampling-based tests, multivariate procedures and much more interesting stuff are treated in this book. People who are interested in the possibilities of problem-solving by simulation (more than in the mathematical fundaments of simulation) will find this book useful. For sure I am going to use simulation in my research more than I used to do...

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Summary: unique book on simulation
Review: I was asked to review this book for an Industrial Engineering Journal and in so doing I took a much closer look at it. I have not changed my opinion but am even more impressed with what Professor Thompson has written so concisely in a book of only 284 pages of text. In addition to providing the philosophy of a statistician and scientist with a wealth of experience, he makes several points that I find that I agree on with him. It is interesting to note his comments on high dimensional computer graphics and even one of his favorite tools non-parametric density estimation in high dimensions. On both topics Professor Thompson feels that the curse of dimensionality is difficult to overcome and we need to pay attention to useful models to guide us in the analysis. He has similar distrust for neural networks and fuzzy set theory. Exploratory analysis with no guiding model is fraught with difficulties!

Although the title is "Simulation", don't get the idea that this is a typical traditional text like say Fishman. Thompson covers many of the same topics but in different and interesting ways. For example the chapter on random quadrature covers most of the Monte Carlo techniques that one can find in Hammersley and Handscomb but he demonstrates the methods as ways to approximate integrals of functions. Although this was an early application of the Monte Carlo method, it is not what we typically do in simulation. But these techniques are still useful and regaining popularity when intensive computing is involved as comes about with bootstrap or Markov chain Monte Carlo. He also shows graphically the pitfalls of some pseudorandom number generators but does not get carried away in the quest to test randomness, a trap that too many of our colleagues fall into.

As Pieter van Gelder pointed out in his review, Thompson stimulates us with some examples of how Monte Carlo methods can readily attack solutions to differential equations such as in the gambler's ruin, the Dirichlet problem and the Fokker-Planck equation.

Thompson's strength is his knowledge of nonparametric density estimation and stochastic processes. Areas in which he has done a great deal of research.

Several authors including Thompson and Dudewicz have noted that the nonparametric bootstrap suffers some because of its discrete jumpy nature. If the distribution that one is sampling from is known to be continuous then smoothing the empiric distribution before resampling makes sense. Dudewicz refers to this approach as "the generalized bootstrap". Thompson and Taylor put a great deal of effort into such a resampling algorithm and named it SIMDAT. Section 5.3 addresses this approach. Thompson also presents SIMEST an algorithm that develops a likelihood function through simulation to then find parameter estimates that approximately maximize this likelihood. He demonstrates this with an oncological example of a stochastic model for tumor growth.

Other very practical and interesting examples of simulation in the text are rank testing for high-dimensional multivariate statistical process control, models for stocks (using geometric Brownian motion)and other problems in finance.

A whole chapter, Chapter 10 is devoted to resampling-based testing of hypotheses and Chapter 9 "Bayesian Approaches" covers Gibbs sampling and Markov chain Monte Carlo. Ideas of experimental design and response surface optimization are covered in Chapters 10 and 11.

Unusual for a statistics text is Chapter 8 that deals with the mathematics of Chaos theory.

Chapter 12 should not be overlooked. This puts many of the techniques together in the study of the AIDS epidemic. This is an endeavor that Professor Thompson has put a great deal of research effort into and his finding about the effects of the homosexual bath houses is very informative and enlightening.

This is a great book for statistician, operation research analysts, scientists and engineers. It contains some valuable material and philosophy that you will find nowhere else!

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Summary: describes statistical modeling from the simulation approach
Review: Professor Thompson writes a very thought provocating book filled with his personal philosophy on model building. It should be taken seriously though, since Professor Thompson has a great deal of experience consulting on real problems particularly for the US Army.

I recommend that the reader go through the preface. It is not the standard preface that outlines the text but rather it introduces arguments justifying the approach. In the preface he describes the Monty Hall problem. This is a wonderful problem for illustrating the subtleties of probability theory. Many mathematicians (including thee famous Paul Erdos) were led to incorrect solutions through probabilistic arguments. Although a careful mathematical treatment would lead to the correct answer, Professor Thompson points out that the easiest way to be convinced of the correct answer is to simulate the game.

The text is fairly technical and is meant for the applied statistician with a strong mathematical and statistical background. For the right audience it is a very entertaining book.

The philosophy is very similar to the philosophy of Efron and other resampling statisticians who see the value in the use of intensive computing to replace analytical methods when the analysis is difficult. The book covers many of the computer-intensive methods that are currently popular including the EM algorithm, Markov Chain Monte Carlo (Gibbs Sampling) and resampling methods including bootstrap. Monte Carlo methods are introduced early (after discussing pseudo random number generation) along with various techniques for variance reduction in the simulations. Then a variety of models and interesting practical examples are presented.

The presentation is not very systematic which may be unsettling for some readers. However, I think it is worth the effort. Any statistician with a broad range of consulting experience will appreciate and relate to Thompson's ideas.