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

A vehicle content portfolio refers to a complete set of combinations of vehicle features offered while satisfying certain restrictions for the vehicle model. Vehicle Content Optimization (VCO) is a...

Uncertainty Quantification in Vehicle Content Optimization for General Motors

In this paper, we will discuss our efforts to create the next generation of semiconductor factory simulation tools, which we call complete response-surface mapping (cRSM). More specifically, we will describe the basic research and software development necessary to produce the capability to provide simulation results on demand for cycle-time measures as a function of throughput and product mix.

Multi-product cycle time and throughput evaluation via simulation on demand

We consider comparing a small, finite number of stochastic systems via computer simulation We use a transformation called batching to change our stochastic systems' data to approximately independent and normally distributed data
Our goal is to find the system with the largest expected performance We achieve this goal by using a class of confidence interval procedures known as Multiple Comparisons with the Best (MCB) MCB is a method that provides joint confidence intervals for the difference between the performance of each individual system and the (unknown) best system Other MCB procedures precede this work, but our procedures uniquely allow for the unknown variances of the data to be different across systems
Unfortunately, an exact solution to our problem for single samples from each system would imply an exact solution to the Behrens-Fisher problem Fortunately, there are a few approximate solutions to the Behrens-Fisher problem, and we extend one of them (the Welch moment approximation) to address our problem In addition, we describe exact (generalized-means) and conservative (means) procedures that require two sampling stages from each system, as is common in simulation studies
The one-stage procedures we derive allow simulators to study their experiments results after the experiments are concluded, but do not provide convenient experimental designs Two stage procedures have advantages over the one-stage procedures: They work with pilot results, require mild variance assumptions, and guarantee inference at a fixed precision Both our one-stage and two-stage procedures could be easily incorporated into simulation packages Although our research focuses on computer simulation experiments, our results apply to other settings including laboratory, work-place, and historical studies Further, this work contributes to Statistics literature by describing heteroscedastic MCB Additionally, MCB is introduced in an alternative manner using Hsu's Lemmas

Heteroscedastic multiple comparison procedures for computer simulation

The paper summarises a conceptual framework for computer-assisted Simulation Experiment Design and Analysis (SEDA). We argue that this SEDA framework is a good one based on its properties. A prototype SEDA CS, which is not described in the paper, is under development for demonstrating the feasibility and appropriateness of this framework.

A conceptual framework for simulation experiment design and analysis

Sensitivity analysis quantifies how a model output responds to variations in its inputs. However, the following sensitivity question has never been rigorously answered: How sensitive is the mean or...

Barry L. Nelson

Papers

Uncertainty Quantification in Vehicle Content Optimization for General Motors

Multi-product cycle time and throughput evaluation via simulation on demand

Heteroscedastic multiple comparison procedures for computer simulation

A conceptual framework for simulation experiment design and analysis

Meaningful sensitivities: A new family of simulation sensitivity measures