Optimal Design for Additive Partially Nonlinear Models PDF Download
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Author: Stefanie Biedermann
Publisher:
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
Author: Stefanie Biedermann
Publisher:
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
Author: Dariusz Ucinski
Publisher: Springer Science & Business Media
ISBN: 331900218X
Category : Mathematics
Languages : en
Pages : 254
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Book Description
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.
Author: Anh Nam Tran
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
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.
Author: Valerii V. Fedorov
Publisher: CRC Press
ISBN: 1439821518
Category : Mathematics
Languages : en
Pages : 404
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Book Description
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.
Author: Peter Goos
Publisher: John Wiley & Sons
ISBN: 1119976162
Category : Science
Languages : en
Pages : 249
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Book Description
"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.
Author: Gang Li
Publisher:
ISBN:
Category :
Languages : en
Pages : 234
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Book Description
Author: Sydney Kwasi Akapame
Publisher:
ISBN:
Category : Genetic algorithms
Languages : en
Pages : 162
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Book Description
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.
Author: S. Silvey
Publisher: Springer Science & Business Media
ISBN: 9400959125
Category : Science
Languages : en
Pages : 94
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Book Description
Prior to the 1970's a substantial literature had accumulated on the theory of optimal design, particularly of optimal linear regression design. To a certain extent the study of the subject had been piecemeal, different criteria of optimality having been studied separately. Also to a certain extent the topic was regarded as being largely of theoretical interest and as having little value for the practising statistician. However during this decade two significant developments occurred. It was observed that the various different optimality criteria had several mathematical properties in common; and general algorithms for constructing optimal design measures were developed. From the first of these there emerged a general theory of remarkable simplicity and the second at least raised the possibility that the theory would have more practical value. With respect to the second point there does remain a limiting factor as far as designs that are optimal for parameter estimation are concerned, and this is that the theory assumes that the model be collected is known a priori. This of course underlying data to is seldom the case in practice and it often happens that designs which are optimal for parameter estimation allow no possibility of model validation. For this reason the theory of design for parameter estimation may well have to be combined with a theory of model validation before its practical potential is fully realized. Nevertheless discussion in this monograph is limited to the theory of design optimal for parameter estimation.
Author: Ehsan Masoudi
Publisher:
ISBN:
Category :
Languages : de
Pages :
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Author: Panos Y. Papalambros
Publisher: Cambridge University Press
ISBN: 1316867455
Category : Technology & Engineering
Languages : en
Pages : 775
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Book Description
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.
