Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. The optimal design for statistical experiments is first formulated as a concave matrix optimization problem. Using tools from convex analysis, the problem is solved generally for a wide class of optimality criteria such as D-, A-, or E-optimality. The book then offers a complementary approach that calls for the study of the symmetry properties of the design problem, exploiting such notions as matrix majorization and the Kiefer matrix ordering. The results are illustrated with optimal designs for polynomial fit models, Bayes designs, balanced incomplete block designs, exchangeable designs on the cube, rotatable designs on the sphere, and many other examples.
Author: Giorgio Celant
Publisher: John Wiley & Sons
Release Date: 2017-04-11
This book considers various extensions of the topics treated in the first volume of this series, in relation to the class of models and the type of criterion for optimality. The regressors are supposed to belong to a generic finite dimensional Haar linear space, which substitutes for the classical polynomial case. The estimation pertains to a general linear form of the coefficients of the model, extending the interpolation and extrapolation framework; the errors in the model may be correlated, and the model may be heteroscedastic. Non-linear models, as well as multivariate ones, are briefly discussed. The book focuses to a large extent on criteria for optimality, and an entire chapter presents algorithms leading to optimal designs in multivariate models. Elfving’s theory and the theorem of equivalence are presented extensively. The volume presents an account of the theory of the approximation of real valued functions, which makes it self-consistent.
Author: Peter Goos
Publisher: John Wiley & Sons
Release Date: 2011-06-28
"This is an engaging and informative book on the modern practice of experimental design. The authors' writing style is entertaining, the consulting dialogs are extremely enjoyable, and the technical material is presented brilliantly but not overwhelmingly. The book is a joy to read. Everyone who practices or teaches DOE should read this book." - Douglas C. Montgomery, Regents Professor, Department of Industrial Engineering, Arizona State University "It's been said: 'Design for the experiment, don't experiment for the design.' This book ably demonstrates this notion by showing how tailor-made, optimal designs can be effectively employed to meet a client's actual needs. It should be required reading for anyone interested in using the design of experiments in industrial settings." —Christopher J. Nachtsheim, Frank A Donaldson Chair in Operations Management, Carlson School of Management, University of Minnesota This book demonstrates the utility of the computer-aided optimal design approach using real industrial examples. These examples address questions such as the following: How can I do screening inexpensively if I have dozens of factors to investigate? What can I do if I have day-to-day variability and I can only perform 3 runs a day? How can I do RSM cost effectively if I have categorical factors? How can I design and analyze experiments when there is a factor that can only be changed a few times over the study? How can I include both ingredients in a mixture and processing factors in the same study? How can I design an experiment if there are many factor combinations that are impossible to run? How can I make sure that a time trend due to warming up of equipment does not affect the conclusions from a study? How can I take into account batch information in when designing experiments involving multiple batches? How can I add runs to a botched experiment to resolve ambiguities? While answering these questions the book also shows how to evaluate and compare designs. This allows researchers to make sensible trade-offs between the cost of experimentation and the amount of information they obtain.
The Department of Statistical Sciences of the University of Bologna in collaboration with the Department of Management and Engineering of the University of Padova, the Department of Statistical Modelling of Saint Petersburg State University, and INFORMS Simulation Society sponsored the Seventh Workshop on Simulation. This international conference was devoted to statistical techniques in stochastic simulation, data collection, analysis of scientific experiments, and studies representing broad areas of interest. The previous workshops took place in St. Petersburg, Russia in 1994, 1996, 1998, 2001, 2005, and 2009. The Seventh Workshop took place in the Rimini Campus of the University of Bologna, which is in Rimini’s historical center.
Experimental design is often overlooked in the literature of applied and mathematical statistics: statistics is taught and understood as merely a collection of methods for analyzing data. Consequently, experimenters seldom think about optimal design, including prerequisites such as the necessary sample size needed for a precise answer for an experimental question. Providing a concise introduction to experimental design theory, Optimal Experimental Design with R: Introduces the philosophy of experimental design Provides an easy process for constructing experimental designs and calculating necessary sample size using R programs Teaches by example using a custom made R program package: OPDOE Consisting of detailed, data-rich examples, this book introduces experimenters to the philosophy of experimentation, experimental design, and data collection. It gives researchers and statisticians guidance in the construction of optimum experimental designs using R programs, including sample size calculations, hypothesis testing, and confidence estimation. A final chapter of in-depth theoretical details is included for interested mathematical statisticians.
Author: J. L. Hodges, Jr.
Release Date: 1970-01-01
Genre: Mathematical statistics
Basic Concepts of Probability and Statistics provides a mathematically rigorous introduction to the fundamental ideas of modern statistics for readers without a calculus background. It is the only book at this level to introduce readers to modern concepts of hypothesis testing and estimation, covering basic concepts of finite, discrete models of probability and elementary statistical methods. Although published in 1970, it maintains a modern outlook, especially in its emphasis on models and model building and also by its coverage of topics such as simple random and stratified survey sampling, experimental design, and nonparametric tests and its discussion of power. The book covers a wide range of applications in manufacturing, biology, and social science, including demographics, political science, and sociology. Among the topics covered that readers may not expect in an elementary text are optimal design and a statement and proof of the fundamental (Neyman-Pearson) lemma for hypothesis testing. Audience: intended for high school and undergraduate students as well as others who want a mathematically rigorous introduction to probability and statistics that does not require calculus. It can supplement high school and college courses on discrete mathematics and will appeal especially to instructors teaching statistics courses within mathematics departments.
Author: Jack P.C. Kleijnen
Publisher: Springer Science & Business Media
Release Date: 2007-11-15
Simulation is a widely used methodology in all Applied Science disciplines. This textbook focuses on this crucial phase in the overall process of applying simulation, and includes the best of both classic and modern methods of simulation experimentation. This book will be the standard reference book on the topic for both researchers and sophisticated practitioners, and it will be used as a textbook in courses or seminars focusing on this topic.
Author: Eugene L. Allgower
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.
Author: Wendell F. Smith
Release Date: 2005-01-01
Genre: Experimental design
Many products, such as foods, personal-care products, beverages, and cleaning agents, are made by mixing ingredients together. This book describes a systematic methodology for formulating such products so that they perform according to one's goals, providing scientists and engineers with a fast track to the implementation of the methodology. Experimental Design for Formulation contains examples from a wide variety of fields and includes a discussion of how to design experiments for a mixture setting and how to fit and interpret models in a mixture setting. It also introduces process variables, the combining of mixture and nonmixture variables in a designed experiment, and the concept of collinearity and the possible problems that can result from its presence. Experimental Design for Formulation is a useful manual for the formulator and can also be used by a resident statistician to teach an in-house short course. Statistical proofs are largely absent, and the formulas that are presented are included to explain how the various software packages carry out the analysis. Many examples are given of output from statistical software packages, and the proper interpretation of computer output is emphasized. Other topics presented include a discussion of an effect in a mixture setting, the presentation of elementary optimization methods, and multiple-response optimization wherein one seeks to optimize more than one response.
Why study the theory of experiment design? Although it can be useful to know about special designs for specific purposes, experience suggests that a particular design can rarely be used directly. It needs adaptation to accommodate the circumstances of the experiment. Successful designs depend upon adapting general theoretical principles to the special constraints of individual applications. Written for a general audience of researchers across the range of experimental disciplines, The Theory of the Design of Experiments presents the major topics associated with experiment design, focusing on the key concepts and the statistical structure of those concepts. The authors keep the level of mathematics elementary, for the most part, and downplay methods of data analysis. Their emphasis is firmly on design, but appendices offer self-contained reviews of algebra and some standard methods of analysis. From their development in association with agricultural field trials, through their adaptation to the physical sciences, industry, and medicine, the statistical aspects of the design of experiments have become well refined. In statistics courses of study, however, the design of experiments very often receives much less emphasis than methods of analysis. The Theory of the Design of Experiments fills this potential gap in the education of practicing statisticians, statistics students, and researchers in all fields.
This well-respected introduction to statistics and statistical theory covers data processing, probability and random variables, utility and descriptive statistics, computation of Bayes strategies, models, testing hypotheses, and much more. 1959 edition.