Optimal Experimental Design For Non Linear Models

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Optimal Experimental Design for Non-Linear Models

Author : Christos P. Kitsos
Publisher : Springer Science & Business Media
ISBN 13 : 3642452876
Total Pages : 104 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Optimal Experimental Design for Non-Linear Models by : Christos P. Kitsos

Download or read book Optimal Experimental Design for Non-Linear Models written by Christos P. Kitsos and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book tackles the Optimal Non-Linear Experimental Design problem from an applications perspective. At the same time it offers extensive mathematical background material that avoids technicalities, making it accessible to non-mathematicians: Biologists, Medical Statisticians, Sociologists, Engineers, Chemists and Physicists will find new approaches to conducting their experiments. The book is recommended for Graduate Students and Researchers.

Optimal Experimental Design for Non-Linear Models

Author : Christos P. Kitsos
Publisher :
ISBN 13 : 9783642452888
Total Pages : 114 pages
Book Rating : 4.4/5 (528 download)

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Book Synopsis Optimal Experimental Design for Non-Linear Models by : Christos P. Kitsos

Download or read book Optimal Experimental Design for Non-Linear Models written by Christos P. Kitsos and published by . This book was released on 2014-01-31 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Optimal Design for Nonlinear Response Models

Author : Valerii V. Fedorov
Publisher : CRC Press
ISBN 13 : 1439821526
Total Pages : 402 pages
Book Rating : 4.4/5 (398 download)

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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

Optimal Design of Experiments

Author : Peter Goos
Publisher : John Wiley & Sons
ISBN 13 : 1119976162
Total Pages : 249 pages
Book Rating : 4.1/5 (199 download)

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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.

Optimal Experimental Design for Nonlinear Models

Author : Monadjemi Farinaz
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (278 download)

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Book Synopsis Optimal Experimental Design for Nonlinear Models by : Monadjemi Farinaz

Download or read book Optimal Experimental Design for Nonlinear Models written by Monadjemi Farinaz and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Optimal Experimental Design for Nonlinear and Generalised Linear Models

Author : James Matthew McGree
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (277 download)

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Book Synopsis Optimal Experimental Design for Nonlinear and Generalised Linear Models by : James Matthew McGree

Download or read book Optimal Experimental Design for Nonlinear and Generalised Linear Models written by James Matthew McGree and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Optimal Design of Experiments

Author : Friedrich Pukelsheim
Publisher : SIAM
ISBN 13 : 0898716047
Total Pages : 527 pages
Book Rating : 4.8/5 (987 download)

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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.

Design of Experiments in Nonlinear Models

Author : Luc Pronzato
Publisher : Springer Science & Business Media
ISBN 13 : 1461463637
Total Pages : 404 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Design of Experiments in Nonlinear Models by : Luc Pronzato

Download or read book Design of Experiments in Nonlinear Models written by Luc Pronzato and published by Springer Science & Business Media. This book was released on 2013-04-10 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Design of Experiments in Nonlinear Models: Asymptotic Normality, Optimality Criteria and Small-Sample Properties provides a comprehensive coverage of the various aspects of experimental design for nonlinear models. The book contains original contributions to the theory of optimal experiments that will interest students and researchers in the field. Practitionners motivated by applications will find valuable tools to help them designing their experiments. The first three chapters expose the connections between the asymptotic properties of estimators in parametric models and experimental design, with more emphasis than usual on some particular aspects like the estimation of a nonlinear function of the model parameters, models with heteroscedastic errors, etc. Classical optimality criteria based on those asymptotic properties are then presented thoroughly in a special chapter. Three chapters are dedicated to specific issues raised by nonlinear models. The construction of design criteria derived from non-asymptotic considerations (small-sample situation) is detailed. The connection between design and identifiability/estimability issues is investigated. Several approaches are presented to face the problem caused by the dependence of an optimal design on the value of the parameters to be estimated. A survey of algorithmic methods for the construction of optimal designs is provided.

Optimal Experimental Design for Nonlinear and Generalised Linear Models

Author : Timothy Hugh Waterhouse
Publisher :
ISBN 13 :
Total Pages : 168 pages
Book Rating : 4.:/5 (297 download)

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Book Synopsis Optimal Experimental Design for Nonlinear and Generalised Linear Models by : Timothy Hugh Waterhouse

Download or read book Optimal Experimental Design for Nonlinear and Generalised Linear Models written by Timothy Hugh Waterhouse and published by . This book was released on 2005 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Design of Experiments

Author : Max Morris
Publisher : CRC Press
ISBN 13 : 1439894906
Total Pages : 376 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Design of Experiments by : Max Morris

Download or read book Design of Experiments written by Max Morris and published by CRC Press. This book was released on 2010-07-27 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offering deep insight into the connections between design choice and the resulting statistical analysis, Design of Experiments: An Introduction Based on Linear Models explores how experiments are designed using the language of linear statistical models. The book presents an organized framework for understanding the statistical aspects of experiment

Optimal Mixture Experiments

Author : B.K. Sinha
Publisher : Springer
ISBN 13 : 8132217861
Total Pages : 213 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis Optimal Mixture Experiments by : B.K. Sinha

Download or read book Optimal Mixture Experiments written by B.K. Sinha and published by Springer. This book was released on 2014-05-24 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book dwells mainly on the optimality aspects of mixture designs. As mixture models are a special case of regression models, a general discussion on regression designs has been presented, which includes topics like continuous designs, de la Garza phenomenon, Loewner order domination, Equivalence theorems for different optimality criteria and standard optimality results for single variable polynomial regression and multivariate linear and quadratic regression models. This is followed by a review of the available literature on estimation of parameters in mixture models. Based on recent research findings, the volume also introduces optimal mixture designs for estimation of optimum mixing proportions in different mixture models, which include Scheffé’s quadratic model, Darroch-Waller model, log- contrast model, mixture-amount models, random coefficient models and multi-response model. Robust mixture designs and mixture designs in blocks have been also reviewed. Moreover, some applications of mixture designs in areas like agriculture, pharmaceutics and food and beverages have been presented. Familiarity with the basic concepts of design and analysis of experiments, along with the concept of optimality criteria are desirable prerequisites for a clear understanding of the book. It is likely to be helpful to both theoreticians and practitioners working in the area of mixture experiments.

Optimum Experimental Designs, With SAS

Author : Anthony Atkinson
Publisher : OUP Oxford
ISBN 13 : 0191537942
Total Pages : 528 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Optimum Experimental Designs, With SAS by : Anthony Atkinson

Download or read book Optimum Experimental Designs, With SAS written by Anthony Atkinson and published by OUP Oxford. This book was released on 2007-05-24 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fitting Models to Biological Data Using Linear and Nonlinear Regression

Author : Harvey Motulsky
Publisher : Oxford University Press
ISBN 13 : 9780198038344
Total Pages : 352 pages
Book Rating : 4.0/5 (383 download)

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Book Synopsis Fitting Models to Biological Data Using Linear and Nonlinear Regression by : Harvey Motulsky

Download or read book Fitting Models to Biological Data Using Linear and Nonlinear Regression written by Harvey Motulsky and published by Oxford University Press. This book was released on 2004-05-27 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most biologists use nonlinear regression more than any other statistical technique, but there are very few places to learn about curve-fitting. This book, by the author of the very successful Intuitive Biostatistics, addresses this relatively focused need of an extraordinarily broad range of scientists.

Functional Approach to Optimal Experimental Design

Author : Viatcheslav B. Melas
Publisher : Springer Science & Business Media
ISBN 13 : 0387316108
Total Pages : 337 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Functional Approach to Optimal Experimental Design by : Viatcheslav B. Melas

Download or read book Functional Approach to Optimal Experimental Design written by Viatcheslav B. Melas and published by Springer Science & Business Media. This book was released on 2006-04-20 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is devoted to studying optimal experimental designs for a wide class of linear and nonlinear regression models. This class includes polynomial, trigonometrical, rational, and exponential models as well as many particular models used in ecology and microbiology. As the criteria of optimality, the well known D-, E-, and c-criteria are implemented. The main idea of the book is to study the dependence of optimal - signs on values of unknown parameters and on the bounds of the design interval. Such a study can be performed on the base of the Implicit Fu- tion Theorem, the classical result of functional analysis. The idea was ?rst introduced in the author’s paper (Melas, 1978) for nonlinear in parameters exponential models. Recently, it was developed for other models in a n- ber of works (Melas (1995, 2000, 2001, 2004, 2005), Dette, Melas (2002, 2003), Dette, Melas, Pepelyshev (2002, 2003, 2004b), and Dette, Melas, Biederman (2002)). Thepurposeofthepresentbookistobringtogethertheresultsobtained and to develop further underlying concepts and tools. The approach, m- tioned above, will be called the functional approach. Its brief description can be found in the Introduction. The book contains eight chapters. The ?rst chapter introduces basic concepts and results of optimal design theory, initiated mainly by J.Kiefer.

Robust and Optimal Experimental Designs for Non-linear Models in Chemical Kinetics

Author : Kieran James Martin
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (16 download)

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Book Synopsis Robust and Optimal Experimental Designs for Non-linear Models in Chemical Kinetics by : Kieran James Martin

Download or read book Robust and Optimal Experimental Designs for Non-linear Models in Chemical Kinetics written by Kieran James Martin and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis considers the problem of selecting robust and optimal experimental designs for accurately estimating the unknown mean parameters of non-linear models in chemical kinetics. The design selection criteria used are local, Bayesian and maximin D-optimality. The thesis focuses on an example provided by GlaxoSmithKline which concerns a chemical reaction where the temperature at which runs of the reaction are conducted and the times at which observations can be made during the reaction are to be varied. Optimal designs for non-linear models are usually dependent on the unknown values of the model parameters. This problem may be overcome by finding designs whose performance is robust to a range of values for each model parameter. Optimal designs are investigated for situations when observations are independent and when correlation exists between observations made on the same run of the process; different forms and strengths of correlation between observations are considered. Designs robust to the correlation and mean parameters are found and assessed via both theoretical measures and a large simulation study which compares the designs found to alternatives currently used in practice. Designs for the situation when the error variables have non-constant variance are obtained by use of a model formed via a power transformation on the response and its expected value. Designs robust to the value of the transformation parameter as well as the correlation and mean parameters are found and assessed. Analytic results are established for obtaining locally D-optimal designs when the model is assumed to have independent observations and the response and expected response have been transformed to remove heteroscedasticity. Where analytic results are not available, numerical methods are used to obtain optimal designs. The differing costs of a run of a reaction and of making an observation on a run are incorporated into design selection. A criterion which includes the cost of the time taken to run a reaction in an experiment is formulated and used to find designs.

Design of Experiments for Generalized Linear Models

Author : Kenneth G. Russell
Publisher : CRC Press
ISBN 13 : 0429614411
Total Pages : 208 pages
Book Rating : 4.4/5 (296 download)

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Book Synopsis Design of Experiments for Generalized Linear Models by : Kenneth G. Russell

Download or read book Design of Experiments for Generalized Linear Models written by Kenneth G. Russell and published by CRC Press. This book was released on 2018-12-14 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Linear Models (GLMs) allow many statistical analyses to be extended to important statistical distributions other than the Normal distribution. While numerous books exist on how to analyse data using a GLM, little information is available on how to collect the data that are to be analysed in this way. This is the first book focusing specifically on the design of experiments for GLMs. Much of the research literature on this topic is at a high mathematical level, and without any information on computation. This book explains the motivation behind various techniques, reduces the difficulty of the mathematics, or moves it to one side if it cannot be avoided, and gives examples of how to write and run computer programs using R. Features The generalisation of the linear model to GLMs Background mathematics, and the use of constrained optimisation in R Coverage of the theory behind the optimality of a design Individual chapters on designs for data that have Binomial or Poisson distributions Bayesian experimental design An online resource contains R programs used in the book This book is aimed at readers who have done elementary differentiation and understand minimal matrix algebra, and have familiarity with R. It equips professional statisticians to read the research literature. Nonstatisticians will be able to design their own experiments by following the examples and using the programs provided.

Nonlinear Regression Modeling for Engineering Applications

Author : R. Russell Rhinehart
Publisher : John Wiley & Sons
ISBN 13 : 1118597966
Total Pages : 402 pages
Book Rating : 4.1/5 (185 download)

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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.