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Introductory remarks about the experiment and its disign. The regression model and methods of estimation. The ordering of designs and the properties of variaces of estimates. Optimality critaria in the regression model. Iterative computation of optimum desings Design of experiments in particular cases. The functional model and measurements of physical fields.
A well-designed experiment is an efficient learning resource. Because experiments in the field and in the laboratory cannot avoid random error, statistical methods are essential for their efficient design and analysis. This book presents the fundamentals of optimum experimental design theory.
This textbook provides a concise introduction to optimal experimental design and efficiently prepares the reader for research in the area. It presents the common concepts and techniques for linear and nonlinear models as well as Bayesian optimal designs. The last two chapters are devoted to particular themes of interest, including recent developments and hot topics in optimal experimental design, and real-world applications. Numerous examples and exercises are included, some of them with solutions or hints, as well as references to the existing software for computing designs. The book is primarily intended for graduate students and young researchers in statistics and applied mathematics who are new to the field of optimal experimental design. Given the applications and the way concepts and results are introduced, parts of the text will also appeal to engineers and other applied researchers.
Experiments in the field and in the laboratory cannot avoid random error and statistical methods are essential for their efficient design and analysis. Authored by leading experts in key fields, this text provides many examples of SAS code, results, plots and tables, along with a fully supported website.
Experiments on patients, processes or plants all have random error, making statistical methods essential for their efficient design and analysis. This book presents the theory and methods of optimum experimental design, making them available through the use of SAS programs. Little previous statistical knowledge is assumed. The first part of the book stresses the importance of models in the analysis of data and introduces least squares fitting and simple optimum experimental designs. The second part presents a more detailed discussion of the general theory and of a wide variety of experiments. The book stresses the use of SAS to provide hands-on solutions for the construction of designs in both standard and non-standard situations. The mathematical theory of the designs is developed in parallel with their construction in SAS, so providing motivation for the development of the subject. Many chapters cover self-contained topics drawn from science, engineering and pharmaceutical investigations, such as response surface designs, blocking of experiments, designs for mixture experiments and for nonlinear and generalized linear models. Understanding is aided by the provision of "SAS tasks" after most chapters as well as by more traditional exercises and a fully supported website. The authors are leading experts in key fields and this book is ideal for statisticians and scientists in academia, research and the process and pharmaceutical industries.
Probability and Statistics theme is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme with contributions from distinguished experts in the field, discusses Probability and Statistics. Probability is a standard mathematical concept to describe stochastic uncertainty. Probability and Statistics can be considered as the two sides of a coin. They consist of methods for modeling uncertainty and measuring real phenomena. Today many important political, health, and economic decisions are based on statistics. This theme is structured in five main topics: Probability and Statistics; Probability Theory; Stochastic Processes and Random Fields; Probabilistic Models and Methods; Foundations of Statistics, which are then expanded into multiple subtopics, each as a chapter. These three volumes are aimed at the following five major target audiences: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs.
Optimum Design 2000
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.
Residualplots 74 Normaland half-normal plots 77 2. 3. 10. TRANSFORMATIONS OF VARIABLES 80 2. 3. 11. WEIGHTED LEAST SQUARES 82 2. 4. Bibliography 84 Appendix A. 2. 1. Basic equation ofthe analysis ofvariance 84 Appendix A. 2. 2. Derivation of the simplified formulae (2. 1 0) and (2. 11) 85 Appendix A. 2. 3. Basic properties ofleast squares estimates 86 Appendix A. 2. 4. Sums ofsquares for tests for lack offit 88 Appendix A. 2. 5. Properties ofthe residuals 90 3. DESIGN OF REGRESSION EXPERIMENTS 96 3. 1. Introduction 96 3. 2. Variance-optimality of response surface designs 98 3. 3. Two Ievel full factorial designs 106 3. 3. 1. DEFINITIONS AND CONSTRUCTION 106 3. 3. 2. PROPERTIES OF TWO LEVEL FULL FACTORIAL DESIGNS 109 3. 3. 3. REGRESSION ANALYSIS OF DAT A OBT AlNED THROUGH TWO LEVEL FULL F ACTORIAL DESIGNS 113 Parameter estimation 113 Effects of factors and interactions 116 Statistical analysis of individual effects and test for lack of fit 118 3. 4. Two Ievel fractional factorial designs 123 3. 4. 1. CONSTRUCTION OF FRACTIONAL F ACTORIAL DESIGNS 123 3. 4. 2. FITTING EQUATIONS TO DATA OBTAlNED BY FRACTIONAL F ACTORIAL DESIGNS 130 3. 5. Bloclung 133 3. 6. Steepest ascent 135 3. 7. Second order designs 142 3. 7. 1. INTRODUCTION 142 3. 7. 2. COMPOSITE DESIGNS 144 Rotatable central composite designs 145 D-optimal composite designs 146 Hartley' s designs 146 3. 7. 3.