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

The focus on mean (long-run average) performance as the primary output measure produced by simulation experiments diminishes the usefulness of simulation for characterizing risk. Confidence intervals on means are often misinterpreted as measures of future risk, when in fact they are measures of error. We introduce the measure of risk & error (MORE) plot as a way to display and make intuitive the concepts of risk and error and thus support sound experiment design and correct decision making.

The more plot: Displaying measures of risk & error from simulation output

When we use simulations to estimate the performance of stochastic systems, the simulation is often driven by input models estimated from finite real-world data. A complete statistical characterization of system performance estimates requires quantifying both input model and simulation estimation errors. The components of input models in many complex systems could be dependent. In this paper, we represent the distribution of a random vector by its marginal distributions and a dependence measure: either product-moment or Spearman rank correlations. To quantify the impact from dependent input model and simulation estimation errors on system performance estimates, we propose a metamodel-assisted bootstrap framework that is applicable to cases when the parametric family of multivariate input distributions is known or unknown. In either case, we first characterize the input models by their moments that are estimated using real-world data. Then, we employ the bootstrap to quantify the input estimation error, and an equation-based stochastic kriging metamodel to propagate the input uncertainty to the output mean, which can also reduce the influence of simulation estimation error due to output variability. Asymptotic analysis provides theoretical support for our approach, while an empirical study demonstrates that it has good finite-sample performance.

Multivariate Input Uncertainty in Output Analysis for Stochastic Simulation

Simulation Methodology for Statisticians, Operations Analysts, and Engineers, Volume I

Naval Research Logistics: Editorial

This dissertation studies optimization of unstructured stochastic simulation problems 
Computer simulation is widely used to model proposed designs, or improve existing designs, of industrial, retail, computer, telecommunications and service systems In most of these complex systems, the output performance measures, such as work in progress, time in queue, or average throughput, are stochastic in nature This stochastic variation makes it more difficult to compare alternative designs Simulation is an evaluative tool; it does not naturally suggest or generate new solutions 
Optimization, on the other hand, is used to seek out the best design from a possibly large number of different combinations of controllable decision variables Most traditional optimization methods, such as linear or integer programming, assume deterministic (as opposed to stochastic) outputs, as well as an underlying mathematical model that can be exploited In a computer simulation of a complex system, however, neither of these assumptions typically hold Researchers have succeeded in adapting a few traditional optimization techniques, such as gradient search, to a simulation setting, but in most cases the simulation model must adhere to a restrictive set of assumptions; in other words, the problem must have a particular structure, such as convexity or continuity 
We have developed theory that allows a heuristic search procedure—a deterministic optimization procedure that does not rely heavily on problem structure—to function in a stochastic environment We also developed theory that allows us to select the true best system from among a large number of stochastic systems This theory is used after the search procedure has run its course We implemented both the search and selection theory into software

Barry L. Nelson

Papers

The more plot: Displaying measures of risk & error from simulation output

Multivariate Input Uncertainty in Output Analysis for Stochastic Simulation

Simulation Methodology for Statisticians, Operations Analysts, and Engineers, Volume I

Naval Research Logistics: Editorial

Search and selection for large-scale stochastic optimization