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Construction Of Optimal Designs For Nonlinear Models
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Author by : Anh Nam Tran
Languange Used : en
Release Date : 2019
Publisher by :
ISBN : OCLC:1357559166
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....
Optimal Design For Nonlinear Response Models
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Author by : Valerii V. Fedorov
Languange Used : en
Release Date : 2013-07-15
Publisher by : CRC Press
ISBN : 9781439821527
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...
Design Of Experiments In Nonlinear Models
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Author by : Luc Pronzato
Languange Used : en
Release Date : 2013-04-10
Publisher by : Springer Science & Business Media
ISBN : 9781461463634
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 Design For Nonlinear Response Models
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Author by : Valerii V. Fedorov
Languange Used : en
Release Date : 2013-07-15
Publisher by : CRC Press
ISBN : 9781439821510
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....
Applied Optimal Designs
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Author by : Martijn P.F. Berger
Languange Used : en
Release Date : 2005-03-11
Publisher by : John Wiley & Sons
ISBN : 0470856971
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....
Parameter Free Designs And Confidence Regions For Nonlinear Models
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Author by : Chinnaphong Bumrungsup
Languange Used : en
Release Date : 1984
Publisher by :
ISBN : OCLC:11628537
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....
An Introduction To Optimal Designs For Social And Biomedical Research
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Author by : Martijn P.F. Berger
Languange Used : en
Release Date : 2009-05-27
Publisher by : John Wiley & Sons
ISBN : 0470746920
The increasing cost of research means that scientists are in more urgent need of optimal design theory to increase the efficiency of parameter estimators and the statistical power of their tests. The objectives of a good design are to provide interpretable and accurate inference at minimal costs. Optimal design theory can help to identify a design with maximum power and maximum information for a statistical model and, at the same time, enable researchers to check on the model assumptions. This Book: Introduces optimal experimental design in an accessible format. Provides guidelines for practitioners to increase the efficiency of their designs, and demonstrates how optimal designs can reduce a study’s costs. Discusses the merits of optimal designs and compares them with commonly used designs. Takes the reader from simple linear regression models to advanced designs for multiple linear regression and nonlinear models in a systematic manner. Illustrates design techniques with practical examples from social and biomedical research to enhance the reader’s understanding. Researchers and students studying social, behavioural and biomedical sciences will find this book useful for understanding design issues and in putting optimal design ideas to practice....
Optimal Experimental Design For Non Linear Models
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Author by : Christos P. Kitsos
Languange Used : en
Release Date : 2014-01-09
Publisher by : Springer Science & Business Media
ISBN : 9783642452871
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....
Finding Optimal Designs For Nonlinear Models Using Metaheuristic Algorithms
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Author by : Ehsan Masoudi
Languange Used : de
Release Date : 2019
Publisher by :
ISBN : OCLC:1190232133
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Applied Optimal Designs
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Author by : Martijn P.F. Berger
Languange Used : en
Release Date : 2005-04-08
Publisher by : John Wiley & Sons
ISBN : 9780470856994
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....