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Optimal Design For Nonlinear Response Models
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Book Synopsis Optimal Design for Nonlinear Response Models by : Valerii V. Fedorov
Download or read book Optimal Design for Nonlinear Response Models written by Valerii V. Fedorov and published by CRC Press. This book was released on 2013-07-15 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal Design for Nonlinear Response Models discusses the theory and applications of model-based experimental design with a strong emphasis on biopharmaceutical studies. The book draws on the authors' many years of experience in academia and the pharmaceutical industry. While the focus is on nonlinear models, the book begins with an explanation of
Book Synopsis Optimal Design for Nonlinear Response Models by : Valerii V. Fedorov
Download or read book Optimal Design for Nonlinear Response Models written by Valerii V. Fedorov and published by CRC Press. This book was released on 2013-07-15 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal Design for Nonlinear Response Models discusses the theory and applications of model-based experimental design with a strong emphasis on biopharmaceutical studies. The book draws on the authors’ many years of experience in academia and the pharmaceutical industry. While the focus is on nonlinear models, the book begins with an explanation of the key ideas, using linear models as examples. Applying the linearization in the parameter space, it then covers nonlinear models and locally optimal designs as well as minimax, optimal on average, and Bayesian designs. The authors also discuss adaptive designs, focusing on procedures with non-informative stopping. The common goals of experimental design—such as reducing costs, supporting efficient decision making, and gaining maximum information under various constraints—are often the same across diverse applied areas. Ethical and regulatory aspects play a much more prominent role in biological, medical, and pharmaceutical research. The authors address all of these issues through many examples in the book.
Book Synopsis Construction of Optimal Designs for Nonlinear Models by : Anh Nam Tran
Download or read book Construction of Optimal Designs for Nonlinear Models written by Anh Nam Tran and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Choosing a good design which can draw a sufficient inference about parameters is essential before conducting an experiment. Dependence between information matrix and model parameters of nonlinear models is an existed conundrum. Seeking optimal design for nonlinear models is our main goal in this thesis. So we start with a general overview of optimal design theory both for linear and nonlinear models. A variety of criteria and their properties are discussed. Some of the bedrock of the theory of optimal design, such as convex design, directional derivatives and general equivalence theorem are considered as well. We review a class of algorithms which are commonly used in practice to search for optimal design of linear models. We then extend these approaches and develop some strategies for constructing optimal designs for nonlinear models. Motivated by the fact that Bayesian methods are ideally suited to contribute to experimental design for nonlinear models, we construct Bayesian optimal designs by incorporating prior information and uncertainties regarding the statistical model. In our Bayesian framework, we consider a discretization of the parameter space to efficiently represent the posterior distribution. We construct optimal designs for some logistic models using a clustering approach and a group sequential multiplicative algorithm. The idea is that, at an appropriate iterate, the single distribution is replaced by conditional distributions within clusters and a marginal distribution across the clusters. Our group sequential method along with the clustering approach provides a novel and powerful method for constructing optimal designs based on nonlinear models. Finally, we develop another novel method in order to obtain prior information on the model parameters by using meta-analysis for constructing optimal designs for nonlinear models. As the prior information on the parameters is rarely known in practice, optimal designs obtained using this method will be more effective in drawing inference for the parameters.
Book Synopsis Optimal Design of Experiments by : Peter Goos
Download or read book Optimal Design of Experiments written by Peter Goos and published by John Wiley & Sons. This book was released on 2011-06-28 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Book Synopsis Optimal Design for Additive Partially Nonlinear Models by : Stefanie Biedermann
Download or read book Optimal Design for Additive Partially Nonlinear Models written by Stefanie Biedermann and published by . This book was released on 2010 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Design of Experiments by : Friedrich Pukelsheim
Download or read book Optimal Design of Experiments written by Friedrich Pukelsheim and published by SIAM. This book was released on 2006-04-01 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applied Optimal Designs by : Martijn P.F. Berger
Download or read book Applied Optimal Designs written by Martijn P.F. Berger and published by John Wiley & Sons. This book was released on 2005-03-11 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an increasing need to rein in the cost of scientific study without sacrificing accuracy in statistical inference. Optimal design is the judicious allocation of resources to achieve the objectives of studies using minimal cost via careful statistical planning. Researchers and practitioners in various fields of applied science are now beginning to recognize the advantages and potential of optimal experimental design. Applied Optimal Designs is the first book to catalogue the application of optimal design to real problems, documenting its widespread use across disciplines as diverse as drug development, education and ground water modelling. Includes contributions covering: Bayesian design for measuring cerebral blood-flow Optimal designs for biological models Computer adaptive testing Ground water modelling Epidemiological studies and pharmacological models Applied Optimal Designs bridges the gap between theory and practice, drawing together a selection of incisive articles from reputed collaborators. Broad in scope and inter-disciplinary in appeal, this book highlights the variety of opportunities available through the use of optimal design. The wide range of applications presented here should appeal to statisticians working with optimal designs, and to practitioners new to the theory and concepts involved.
Book Synopsis Robust and Optimal Design Strategies for Nonlinear Models Using Genetic Algorithms by : Sydney Kwasi Akapame
Download or read book Robust and Optimal Design Strategies for Nonlinear Models Using Genetic Algorithms written by Sydney Kwasi Akapame and published by . This book was released on 2014 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Experimental design pervades all areas of scientific inquiry. The central idea behind many designed experiments is to improve or optimize inference about the quantities of interest in a statistical model. Thus, the strengths of any inferences made will be dependent on the choice of the experimental design and the statistical model. Any design that optimizes some statistical property will be referred to as an optimal design. In the main, most of the literature has focused on optimal designs for linear models such as low-order polynomials. While such models are widely applicable in some areas, they are unsuitable as approximations for data generated by systems or mechanisms that are nonlinear. Unlike linear models, nonlinear models have the unique property that the optimal designs for estimating their model parameters depend on the unknown model parameters. This dissertation addresses several strategies to choose experimental designs in nonlinear model situations. Attempts at solving the nonlinear design problem have included locally optimal designs, sequential designs and Bayesian optimal designs. Locally optimal designs are optimal designs conditional on a particular guess of the parameter vector. Although these designs are useful in certain situations, they tend to be sub-optimal if the guess is far from the truth. Sequential designs are based on repeated experimentation and tend to be expensive. Bayesian optimal designs generalize locally optimal designs by averaging a design optimality criterion over a prior distribution, but tend to be sensitive to the choice of prior distribution. More importantly, in cases where multiple priors are elicited from a group of experts, designs are required that are robust to the class (or range) of prior distributions. New robust design criteria to address the issue of robustness are proposed in this dissertation. In addition, designs based on axiomatic methods for pooling prior distributions are obtained. Efficient algorithms for generating designs are also required. In this research, genetic algorithms (GAs) are used for design generation in the MATLAB® computing environment. A new genetic operator suited to the design problem is developed and used. Existing designs in the published literature are improved using GAs.
Book Synopsis Response Surfaces: Designs and Analyses by : Andre I. Khuri
Download or read book Response Surfaces: Designs and Analyses written by Andre I. Khuri and published by Routledge. This book was released on 2018-12-18 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Response Surfaces: Designs and Analyses; Second Edition presents techniques for designing experiments that yield adequate and reliable measurements of one or several responses of interest, fitting and testing the suitability of empirical models used for acquiring information from the experiments, and for utilizing the experimental results to make decisions concerning the system under investigation. This edition contains chapters on response surface models with block effects and on Taguchi's robust parameter design, additional details on transformation of response variable, more material on modified ridge analysis, and new design criteria, including rotatability for multiresponse experiments. It also presents an innovative technique for displaying correlation among several response. Numerical examples throughout the book plus exercises--with worked solutions to selected problems--complement the text.
Book Synopsis Finding optimal designs for nonlinear models using metaheuristic algorithms by : Ehsan Masoudi
Download or read book Finding optimal designs for nonlinear models using metaheuristic algorithms written by Ehsan Masoudi and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis D-optimal Designs for a Class of Nonlinear Models by : Paul Joseph Lupinacci
Download or read book D-optimal Designs for a Class of Nonlinear Models written by Paul Joseph Lupinacci and published by . This book was released on 2001 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinearity Curvature Measurement and Optimal Designs in Nonlinear Regression Models by : Jieru Xie
Download or read book Nonlinearity Curvature Measurement and Optimal Designs in Nonlinear Regression Models written by Jieru Xie and published by . This book was released on 2009 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation research, a novel, practical method of assessing nonlinearity behavior is developed to assess the extent of the nonlinearity in a nonlinear regression model with data points. We consider the geometric aspects of nonlinear regression modeling and use the familiar concept of confidence level as the criterion for nonlinearity assessment. The computation is based on the comparison of the linear approximation inference ellipsoid region and the likelihood region, the often "banana-shaped" confidence region computed without the linear assumption. We tested our method on some real datasets and compared our results with other methods. It is found that the new method, CLAN ( C onfidence L evel A ssessment of N onlinearity), is in good agreement with the root mean squared estimates of parameter effects and intrinsic nonlinearity introduced by Bates & Watts in their 1980s paper and book. Since the nonlinearity is related to the experimental design, we also study the optimal experimental designs for nonlinear models which are mainly derived from PK/PD models in phase I clinical trial analysis. We use the D-optimal criterion which is to maximize the determinant of the information matrix for the parameters in the model. For nonlinear models, the optimal design is only locally optimal for preliminary conjecture about parameters. We investigate a sequential approach in which experimentation is carried out in stages and inference made on [straight theta] after each stage. The simulation results show that as the sequential stage increases, the support points given by local D-optimal (LD) designs converge to the design under the [straight theta] true . We investigate two sequential design approaches: (1) simple sequential design, and (2) batch sequential design. Simulation results show that the batch sequential design can provide better parameter estimates than the simple sequential design. We also propose a new robust, near-optimal design with extra support points--the unequally expanded spaced local D-optimal design (UESLD) and apply the method to a real dose-response dataset. Simulation results show that the new UESLD design can yield better parameter estimates compared with the original design; also, the nonlinearity curvature behavior can be improved by using the UESLD design. Key words. Nonlinear regression; Nonlinearity curvatures; Pharmacokinetics; Optimum experimental designs; D-optimality.
Book Synopsis mODa 9 – Advances in Model-Oriented Design and Analysis by : Alessandra Giovagnoli
Download or read book mODa 9 – Advances in Model-Oriented Design and Analysis written by Alessandra Giovagnoli and published by Springer Science & Business Media. This book was released on 2010-06-10 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statisticians and experimentalists will find the latest trends in optimal experimental design research. Some papers are pioneering contributions, leading to new open research problems. It is a colection of peer reviewed papers.
Book Synopsis Nonlinear Regression Modeling for Engineering Applications by : R. Russell Rhinehart
Download or read book Nonlinear Regression Modeling for Engineering Applications written by R. Russell Rhinehart and published by John Wiley & Sons. This book was released on 2016-09-26 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since mathematical models express our understanding of how nature behaves, we use them to validate our understanding of the fundamentals about systems (which could be processes, equipment, procedures, devices, or products). Also, when validated, the model is useful for engineering applications related to diagnosis, design, and optimization. First, we postulate a mechanism, then derive a model grounded in that mechanistic understanding. If the model does not fit the data, our understanding of the mechanism was wrong or incomplete. Patterns in the residuals can guide model improvement. Alternately, when the model fits the data, our understanding is sufficient and confidently functional for engineering applications. This book details methods of nonlinear regression, computational algorithms,model validation, interpretation of residuals, and useful experimental design. The focus is on practical applications, with relevant methods supported by fundamental analysis. This book will assist either the academic or industrial practitioner to properly classify the system, choose between the various available modeling options and regression objectives, design experiments to obtain data capturing critical system behaviors, fit the model parameters based on that data, and statistically characterize the resulting model. The author has used the material in the undergraduate unit operations lab course and in advanced control applications.
Book Synopsis Parameter-free Designs and Confidence Regions for Nonlinear Models by : Chinnaphong Bumrungsup
Download or read book Parameter-free Designs and Confidence Regions for Nonlinear Models written by Chinnaphong Bumrungsup and published by . This book was released on 1984 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The choice of an optimal design for parameter estimation in a nonlinear model depends on the values of the model's parameters. This is an undesirable feature since such a design is used to estimate the same parameter values which are needed for its derivation. To overcome this difficulty a method is developed for the construction of a nonlinear design which does not depend on the nonlinear model's parameters. Such a design is called a parameter-free design. This method is an extension of A.I. Khuri's modified D-optimality criterion (Parameter-Free Designs for Nonlinear Models. Technical Report No. 188, Department of Statistics, University of Florida, Gainesville, Florida, 1982). It is based on using a proper approximation of the true mean response function described in the nonlinear model with either Lagrange or spline interpolating polynomials. Each approximation will be used to derive a parameter-free design. Optimal designs obtained on the basis of these interpolating polynomials depend on the size of the error associated with the approximation of the true mean response. A method for the construction of a confidence region on the vector of parameters in a nonlinear model is also developed. Unlike most other methods which are available for that purpose, this method does not require specifying initial estimates of the parameters. The aforementioned confidence region can be used to obtain simultaneous confidence intervals on the nonlinear model's parameters. These intervals, however, are conservative in the sense that their joint confidence coefficient cannot be less than a preset value.
Book Synopsis First-order Optimal Designs for Non Linear Models by : Paola Sebastiani
Download or read book First-order Optimal Designs for Non Linear Models written by Paola Sebastiani and published by . This book was released on 1996 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Response Surface Methodology by : Raymond H. Myers
Download or read book Response Surface Methodology written by Raymond H. Myers and published by John Wiley & Sons. This book was released on 2016-01-04 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Third Edition: “This new third edition has been substantially rewritten and updated with new topics and material, new examples and exercises, and to more fully illustrate modern applications of RSM.” - Zentralblatt Math Featuring a substantial revision, the Fourth Edition of Response Surface Methodology: Process and Product Optimization Using Designed Experiments presents updated coverage on the underlying theory and applications of response surface methodology (RSM). Providing the assumptions and conditions necessary to successfully apply RSM in modern applications, the new edition covers classical and modern response surface designs in order to present a clear connection between the designs and analyses in RSM. With multiple revised sections with new topics and expanded coverage, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Fourth Edition includes: Many updates on topics such as optimal designs, optimization techniques, robust parameter design, methods for design evaluation, computer-generated designs, multiple response optimization, and non-normal responses Additional coverage on topics such as experiments with computer models, definitive screening designs, and data measured with error Expanded integration of examples and experiments, which present up-to-date software applications, such as JMP®, SAS, and Design-Expert®, throughout An extensive references section to help readers stay up-to-date with leading research in the field of RSM An ideal textbook for upper-undergraduate and graduate-level courses in statistics, engineering, and chemical/physical sciences, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Fourth Edition is also a useful reference for applied statisticians and engineers in disciplines such as quality, process, and chemistry.
