Simulation and the Monte Carlo Method

杨利霞

Simulation and the Monte Carlo Method


This book, which is in the Wiley Series in Probability and
Mathematical Statistics, deals with statistical aspects of simulation
and Monte Carlo methods. In the preface, the author states that he
assumes the readers “are familiar with the basic concepts of prob
ability theory, mathematical statistics, integral and differential
equations, and that they have an elementary knowledge of vector
and matrix operators.” In addition, the reader should have some
knowledge of stationary stochastic processes, especially Markov
processes, and be familiar with elementary queuing models.
The book has seven chapters. Chapter 1 provides a general
introduction to the ideas of systems models and simulation. Basic
methods for random-number generation on the computer are in
troduced and compared in Chapter 2. This chapter also includes a
brief discussion of some tests for randomness of random-number
streams. Chapter 3 provides an extensive presentation of random
variate generation that is both well structured and readable.
The first part of Chapter 4 deals with Monte Carlo integration
techniques, and in the last part of the chapter the author applies
various variance reduction techniques to the problem of Monte
Carlo integration. Chapter 5 contains a rather obscure discussion
of Monte Carlo methods for the solution of linear equations and
integral equations. Although this topic is likely to be of much
interest to physicists and a few applied mathematicians, it seemed
to be out of place in this book.
In Chapter 6, the author gives an extensive treatment of the
regenerative method for simulation analysis. This chapter draws
heavily from the recent work of three people: Iglehart, Heidelber
ger, and Lavenberg. The chapter presents an understandable dis
cussion of the regenerative method and includes some of the
author’s own research on methods for selecting the best stable
stochastic system. The chapter ends with a discussion of two vari
ance reduction techniques applicable to the regenerative method:
control variates and common random-number streams. In Chapter
7, the author presents some of his own research concerning Monte
Carlo methods for the solution of complex nonconvex optimization
problems.
This book is clearly not an elementary textbook on simulation.
Quite the contrary, the background required of the reader is exten
sive. Measure theoretic terminology is sprinkled throughout (al
though measure theory is not required in any proofs). The book
does not require any background in simulation methodology, how
ever. The author has included proofs of all major results and has
neatly summarized all algorithms presented in the text.
The selection of topics in this book is unusual. On the one hand,
the author includes chapters on Monte Carlo solution of linear
equations and Monte Carlo optimization, while on the other hand,
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BOOK REVIEWS
the important and pragmatic topics of time series and sequential
estimation methods are omitted entirely. This book could be a text
for a theoretically oriented course in simulation for advanced
graduate students. However, it would need to be supplemented by
another text or class notes if the course included the topics of time
series or sequential methods.
This is a good book-well
organized and readable. However, it
could have been better if the level of the book were reduced some
what and if a more useful selection of topics had been included.
Nevertheless, it is recommended for persons who do research in
simulation methodology and for those who apply simulation meth
odology to various problem areas in mathematics, statistics, engin
eermg, and operations research.