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 paper provides an advanced tutorial on the construction of ranking-and-selection procedures for selecting the best simulated system. We emphasize procedures that provide a guaranteed probability of correct selection, and the key theoretical results that are used to derive them.

Selecting the best system: selecting the best system: theory and methods

This paper introduces a method to model and simulate non-stationary, non-renewal arrival processes that depends only on the analyst setting intuitive and easily controllable parameters. Thus, it is suitable for assessing the impact of non-stationary, non-exponential, and non-independent arrivals on simulated performance when they are suspected. A specific implementation of the method is also described and provided for download.

http://users.iems.northwestern.edu/~nelsonb/Publications/NelsonGerhardt.pdf

Modelling and simulating non-stationary arrival processes to facilitate analysis

This panel discusses goals and educational strategies for teaching simulation in academia. Clearly, there is considerable material to cover in a single course or a sequence thereof in, say, an undergraduate program. The issue is how to motivate and empower students to analyze complex problems correctly and to prevent the pitfall of misusing the concept.

Panel: academic perspectives: various ways academics teach simulation: are they all appropriate?

“Virtual statistics,” as we define them, are estimators of performance measures that are conditional on the occurrence of an event; virtual waiting time of a customer arriving to a queue at time τ0...

Virtual Statistics in Simulation via k Nearest Neighbors

A simulation model is composed of inputs and logic; the inputs represent the uncertainty or randomness in the system, while the logic determines how the system reacts to the uncertain elements. Simple input models, consisting of independent and identically distributed sequences of random variates from standard probability distributions, are included in every commercial simulation language. Software to fit these distributions to data is also available. In this tutorial we describe input models that are useful when simple models are not.

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Barry L. Nelson

Papers

Selecting the best system: selecting the best system: theory and methods

Modelling and simulating non-stationary arrival processes to facilitate analysis

Panel: academic perspectives: various ways academics teach simulation: are they all appropriate?

Virtual Statistics in Simulation via k Nearest Neighbors

Input modeling when simple models fail