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:

Download or read book mODa 10 Advances in Model Oriented Design and Analysis written by Dariusz Ucinski and published by Springer Science & Business Media. This book was released on 2013-03-21 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the proceedings of the 10th Workshop on Model-Oriented Design and Analysis (mODa). A model-oriented view on the design of experiments, which is the unifying theme of all mODa meetings, assumes some knowledge of the form of the data-generating process and naturally leads to the so-called optimum experimental design. Its theory and practice have since become important in many scientific and technological fields, ranging from optimal designs for dynamic models in pharmacological research, to designs for industrial experimentation, to designs for simulation experiments in environmental risk management, to name but a few. The methodology has become even more important in recent years because of the increased speed of scientific developments, the complexity of the systems currently under investigation and the mounting pressure on businesses, industries and scientific researchers to reduce product and process development times. This increased competition requires ever increasing efficiency in experimentation, thus necessitating new statistical designs. This book presents a rich collection of carefully selected contributions ranging from statistical methodology to emerging applications. It primarily aims to provide an overview of recent advances and challenges in the field, especially in the context of new formulations, methods and state-of-the-art algorithms. The topics included in this volume will be of interest to all scientists and engineers and statisticians who conduct experiments.

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.

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.

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.

Download or read book Locally D optimal Designs for Nonlinear Models with Minimal Number of Support Points written by Gang Li and published by . This book was released on 2005 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

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:

Download or read book Globally Optimal Design written by Douglass J. Wilde and published by John Wiley & Sons. This book was released on 1978 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.

Download or read book Contributions to the Design and Analysis of Non linear Models written by Chih-Ling Tsai and published by . This book was released on 1983 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Principles of Optimal Design written by Panos Y. Papalambros and published by Cambridge University Press. This book was released on 2017-01-09 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: Design optimization is a standard concept in engineering design, and in other disciplines which utilize mathematical decision-making methods. This textbook focuses on the close relationship between a design problem's mathematical model and the solution-driven methods which optimize it. Along with extensive material on modeling problems, this book also features useful techniques for checking whether a model is suitable for computational treatment. Throughout, key concepts are discussed in the context of why and when a particular algorithm may be successful, and a large number of examples demonstrate the theory or method right after it is presented. This book also contains step-by-step instructions for executing a design optimization project - from building the problem statement to interpreting the computer results. All chapters contain exercises from which instructors can easily build quizzes, and a chapter on 'principles and practice' offers the reader tips and guidance based on the authors' vast research and instruction experience.

Download or read book D optimal Designs for a Nonlinear Model with Independent Errors and Repeated Measures written by Jennifer Lou Aquino Kendall and published by . This book was released on 1994 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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:

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.

Download or read book D optimal Designs for Complex Nonlinear Models in Chemical Kinetics PK PD and Environmental Science written by Ying Zhou and published by . This book was released on 2010 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Partially Linear Models written by Wolfgang Härdle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.

Download or read book A optimal design measures for one way layouts with additive regression written by Werner Wierich and published by . This book was released on 1986 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: