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

Controlled sequential bifurcation (CSB) is a factor-screening method for discrete-event simulations. It combines a multistage hypothesis testing procedure with the original sequential bifurcation procedure to control both the power for detecting important effects at each bifurcation step and the Type I error for each unimportant factor under heterogeneous variance conditions when a main-effects model applies. This paper improves the CSB procedure in two aspects. First, a new fully sequential hypothesis-testing procedure is introduced that greatly improves the efficiency of CSB. Moreover, this paper proposes CSB-X, a more general CSB procedure that has the same error control for screening main effects that CSB does, even when two-factor interactions are present. The performance of the new method is proven and compared with the original CSB procedure.

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

Improving the Efficiency and Efficacy of Controlled Sequential Bifurcation for Simulation Factor Screening

This paper lays the foundation for employing Gaussian Markov random fields (GMRFs) for discrete decision–variable optimization via simulation; that is, optimizing the performance of a simulated sys...

Gaussian Markov Random Fields for Discrete Optimization via Simulation: Framework and Algorithms

We evaluate, theoretically and empirically, the power of a family of tests for initial-condition bias.

/pdf/evaluation-of-tests-for-initial-condition-bias-2bebuqpodf.pdf

Evaluation of tests for initial-condition bias

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 the input modeling problem is more complex.

/pdf/input-modeling-tools-for-complex-problems-4y3ubcaykh.pdf

Input modeling tools for complex problems

Whereas multiple comparisons computations in a one-way model are well understood, multiple comparisons computations in a general linear model (GLM) are not. For models with the so-called “one-way structure,” no new technique is needed beyond proper substitution of terms. Examples of designs that guarantee a one-way structure include variance balanced designs and orthogonal designs. For models without a one-way structure, more sophisticated computational techniques are needed. Approximations based on the probabilistic inequalities of Bonferroni, Sidak, and Slepian are too conservative. Even the second-order Hunter—Worsley inequality is rather conservative. The so-called factor analytic approximation is quite accurate for multiple comparison with a control (MCC) and multiple comparison with the best (MCB), but conditions for it to be conservative are not known. This article describes a highly accurate, deterministic, conservative approximation that is applicable to a popular class of general linear...

Barry L. Nelson

Papers

Improving the Efficiency and Efficacy of Controlled Sequential Bifurcation for Simulation Factor Screening

Gaussian Markov Random Fields for Discrete Optimization via Simulation: Framework and Algorithms

Evaluation of tests for initial-condition bias

Input modeling tools for complex problems

Multiple Comparisons in the General Linear Model