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

We describe methods for estimating the variance of the sample mean of a steady-state simulation output process using correlation-based methods, all involving some form of “batching”. Since no single method dominates all others across all measures of performance, we provide a framework for asymptotic comparison of such estimators. Research challenges are also identified.

Chapter 15 Correlation-Based Methods for Output Analysis

When a customer arrives to a service system, how long should they expect to wait, and how long might their wait actually be? Computer simulation is an ideal tool for answering such questions for very general and complex queueing systems, but they are not always answered by the automatic statistical summary generated by commercial simulation languages. Using an illustration based on passenger check-in at an airport, we demonstrate how standard summary measures go wrong and provide methods that correctly answer these questions.

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Estimating and interpreting the waiting time for customers arriving to a non-stationary queueing system

Screening experiments are performed to eliminate unimportant factors so that the remaining important factors can be more thoroughly studied in later experiments. Sequential bifurcation (SB) is a screening method that is well suited for simulation experiments; the challenge is to prove the "correctness" of the results. This paper proposes Controlled Sequential Bifurcation (CSB), a procedure that incorporates a two-stage hypothesis-testing approach into SB to control error and power. A detailed algorithm is given, performance is proved and an empirical evaluation is presented.

Issues on simulation and optimization I: controlled sequential bifurcation: a new factor-screening method for discrete-event simulation

We introduce the topic of this book, explain what we mean by stochastic computer simulation and provide examples of application areas. We motivate the remaining chapters in the book through two in-depth examples. These examples also help clarify several concepts and techniques that are pervasive in simulation theory and practice.

Chapter 1 Stochastic Computer Simulation

"Virtual statistics" are performance measures that are conditional on the occurrence of an event; virtual waiting time of a customer arriving to a queue at time t is one example. In this paper, we describe a k-nearest-neighbor method for estimating virtual statistics post-simulation from the retained sample paths, examining both its small-sample and asymptotic properties. We implement leave-one-replication-out cross validation for tuning the parameter k, and compare the prediction performance of the k-nearest-neighbor estimator with a time-bucket estimator.

Barry L. Nelson

Papers

Chapter 15 Correlation-Based Methods for Output Analysis

Estimating and interpreting the waiting time for customers arriving to a non-stationary queueing system

Issues on simulation and optimization I: controlled sequential bifurcation: a new factor-screening method for discrete-event simulation

Chapter 1 Stochastic Computer Simulation

Simulation analytics for virtual statistics via k nearest neighbors