THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Statistics for Spatial Data.

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Convex Analysisの二,三の進展について

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

This tutorial describes basic principles for designing st artistically efficient simulation experiments and controlling experiment error, including the use of explorat or y experiments, assignment of random number seeds or streams, and analysis of the results. Simulation experiments that are performed to compare two or more systems are emphasized.

Designing efficient simulation experiments

A batch-size analysis is presented which provides the framework for an algorithm to form MCB (multiple comparisons with the best) confidence intervals for steady-state simulations. Empirical studies indicate that the proposed heuristic approach to the batching problem is effective. >

Batch-size effects on simulation optimization using multiple comparisons with the best

The indifference-zone (IZ) formulation of ranking and selection (R&S) is the foundation of many procedures that have been useful for choosing the best among a finite number of simulated alternatives. Of course, simulation models are imperfect representations of reality, which means that a simulation-based decision, such as choosing the best alternative, is subject to model risk. In this paper we explore the impact of model risk due to input uncertainty on IZ R&S. "Input uncertainty" is the result of having estimated ("fit") the simulation input models to observed real-world data. We find that input uncertainty may force the user to revise, or even abandon, their objectives when employing a R&S procedure, or it may have very little effect on selecting the best system even when the marginal input uncertainty is substantial.

Input uncertainty and indifference-zone ranking & selection

Selecting the solution with the largest or smallest mean of a primary performance measure from a finite set of solutions while requiring secondary performance measures to satisfy certain constraints is called constrained selection of the best CSB in the simulation ranking and selection literature. In this paper, we consider CSB problems with secondary performance measures that must satisfy probabilistic constraints, and we call such problems chance constrained selection of the best CCSB. We design procedures that first check the feasibility of all solutions and then select the best among all the sample feasible solutions. We prove the statistical validity of these procedures for variations of the CCSB problem under the indifference-zone formulation. Numerical results show that the proposed procedures can efficiently handle CCSB problems with up to 100 solutions, each with five chance constraints.

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Chance Constrained Selection of the Best

The purpose of simulation, at least in this book, is to estimate the values of performance measures of a stochastic system by conducting a statistical experiment on a computer model of it. This chapter describes principles and methods for the design and analysis of that experiment.

Barry L. Nelson

Papers

Designing efficient simulation experiments

Batch-size effects on simulation optimization using multiple comparisons with the best

Input uncertainty and indifference-zone ranking & selection

Chance Constrained Selection of the Best

Experiment Design and Analysis