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Statistical tools for simulation practitioners. (English) Zbl 0629.62004

Statistics: Textbooks and Monographs, Vol. 76. New York-Basel: Marcel Dekker, Inc. XII, 429 p. (1987).
This book is concerned with statistical design and analysis necessary for simulation practioners. It consists of 30 chapters and exercises, and is divided into three parts. Part I discusses tactical statistical issues which arise in stochastic simulation experiments; how long we should continue a specific simulation run and how we determine the accuracy of the simulation runs when we have stopped the simulation run. The remaining two parts, Part II.A and II.B, discuss the strategic issues; which variants of the simulation model we actually run (experimental design) and how we can analyze the output data (regression analysis).
Part I (Runlength and confidence intervals) consists of 8 chapters. Following an introduction in Chapter 1 (5 pages), Chapter 2 (6 pages) defines terminating and nonterminating simulations. Several procedures for the estimation of the mean of a distribution and estimation of difference of two means are presented in Chapters 3 (14 pages) and 4 (18 pages), respectively. Chapter 5 (12 pages) mainly discusses the length of the simulation run required to estimate a single mean or some other single response. Steady-state concepts are briefly discussed in Chapter 6 (5 pages). Chapter 7 (11 pages) presents several techniques of terminating, and steady-state simulations. Chapter 8 (3 pages) summarizes applications of statistical techniques in simulation.
Part II.A (Regression analysis) begins with a brief introduction (Chapter 9 (2 pages)). Chapter 10 (12 pages) defines types of variables appearing in regression analysis, and Chapter 11 (4 pages) introduces formal metamodels. Basic results of regression analysis are summarized in Chapter 12 (7 pages), and assumptions in least squares methods are discussed and some alternatives to least squares are presented in Chapter 13 (39 pages). How to revise a false regression model is presented in Chapter 14 (5 pages). Chapter 15 (5 pages) introduces response surface methodology and discusses optimization of simulation models. Miscellaneous topics in Chapter 16 (3 pages) are followed by two case studies in Chapter 17 (7 pages). Important formulas of Part II.A are summarized in Chapter 18 (3 pages).
Chapter 19 (3 pages) provides the introduction of experimental designs discussed in Part II.B (Experimental design). An example in Chapter 20 (10 pages) demonstrates three approaches to the design of experiments. Basic concepts of experimental design are inroduced in the following chapters; linear models are given in Chapter 21 (8 pages), and the concept of interactions is defined in Chapter 22 (5 pages). To analyze experimental data, analysis of variance (ANOVA) is discussed in Chapter 23 (9 pages). Chapters 24 (7 pages) and 25 (11 pages) provide incomplete designs. Response surface designs useful to quantitative factors are discussed in Chapter 26 (5 pages). Chapter 27 (3 pages) comments on other types of designs. Designs for the case with too many factors are given in Chapter 28 (9 pages) and stagewise experimentation is discussed in Chapter 29 (5 pages). Chapter 30 (7 pages) concludes Part II.B with a discussion of several criteria for judging experiments.
At the end of each part, exercises, notes on references and solutions to exercises are provided to help the readers’ understanding. More than 700 references listed up at the end of the book make this book a good reference to simulation practitioners.
Reviewer: K.Uosaki

MSC:

62-02 Research exposition (monographs, survey articles) pertaining to statistics
65C20 Probabilistic models, generic numerical methods in probability and statistics
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
62K99 Design of statistical experiments
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62J99 Linear inference, regression
62P99 Applications of statistics