Optimal Bayesian Experimental Design In The Presence Of Model Error
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| Author | : Peter Goos |
| Publisher | : John Wiley & Sons |
| Total Pages | : 249 |
| Release | : 2011-06-28 |
| Genre | : Science |
| ISBN | : 1119976162 |
"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 | : Dieter Rasch |
| Publisher | : CRC Press |
| Total Pages | : 345 |
| Release | : 2011-05-18 |
| Genre | : Mathematics |
| ISBN | : 1439816980 |
Experimental design is often overlooked in the literature of applied and mathematical statistics: statistics is taught and understood as merely a collection of methods for analyzing data. Consequently, experimenters seldom think about optimal design, including prerequisites such as the necessary sample size needed for a precise answer for an experi
| Author | : Herman Chernoff |
| Publisher | : SIAM |
| Total Pages | : 124 |
| Release | : 1972-01-01 |
| Genre | : Technology & Engineering |
| ISBN | : 9781611970593 |
An exploration of the interrelated fields of design of experiments and sequential analysis with emphasis on the nature of theoretical statistics and how this relates to the philosophy and practice of statistics.
| Author | : Andrew Gelman |
| Publisher | : CRC Press |
| Total Pages | : 677 |
| Release | : 2013-11-01 |
| Genre | : Mathematics |
| ISBN | : 1439840954 |
Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.
| Author | : Friedrich Pukelsheim |
| Publisher | : SIAM |
| Total Pages | : 527 |
| Release | : 2006-04-01 |
| Genre | : Mathematics |
| ISBN | : 0898716047 |
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.
| Author | : Valerii V. Fedorov |
| Publisher | : CRC Press |
| Total Pages | : 402 |
| Release | : 2013-07-15 |
| Genre | : Mathematics |
| ISBN | : 1439821526 |
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
| Author | : Claus Beisbart |
| Publisher | : Springer |
| Total Pages | : 1056 |
| Release | : 2019-04-09 |
| Genre | : Computers |
| ISBN | : 3319707663 |
This unique volume introduces and discusses the methods of validating computer simulations in scientific research. The core concepts, strategies, and techniques of validation are explained by an international team of pre-eminent authorities, drawing on expertise from various fields ranging from engineering and the physical sciences to the social sciences and history. The work also offers new and original philosophical perspectives on the validation of simulations. Topics and features: introduces the fundamental concepts and principles related to the validation of computer simulations, and examines philosophical frameworks for thinking about validation; provides an overview of the various strategies and techniques available for validating simulations, as well as the preparatory steps that have to be taken prior to validation; describes commonly used reference points and mathematical frameworks applicable to simulation validation; reviews the legal prescriptions, and the administrative and procedural activities related to simulation validation; presents examples of best practice that demonstrate how methods of validation are applied in various disciplines and with different types of simulation models; covers important practical challenges faced by simulation scientists when applying validation methods and techniques; offers a selection of general philosophical reflections that explore the significance of validation from a broader perspective. This truly interdisciplinary handbook will appeal to a broad audience, from professional scientists spanning all natural and social sciences, to young scholars new to research with computer simulations. Philosophers of science, and methodologists seeking to increase their understanding of simulation validation, will also find much to benefit from in the text.
| Author | : Alessandro Di Bucchianico |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 239 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3790826936 |
The volume contains the proceedings of the 7th Workshop on Model-Oriented Design and Analysis which has had the purpose of bringing together leading researchers in Eastern and Western Europe for an in-depth discussion of the optimal design of experiments. The papers are representative of the latest developments concerning non-linear models, computational algorithms and important applications, especially to medical statistics.
| Author | : Pijush Samui |
| Publisher | : Butterworth-Heinemann |
| Total Pages | : 592 |
| Release | : 2019-10-05 |
| Genre | : Computers |
| ISBN | : 0128165464 |
Handbook of Probabilistic Models carefully examines the application of advanced probabilistic models in conventional engineering fields. In this comprehensive handbook, practitioners, researchers and scientists will find detailed explanations of technical concepts, applications of the proposed methods, and the respective scientific approaches needed to solve the problem. This book provides an interdisciplinary approach that creates advanced probabilistic models for engineering fields, ranging from conventional fields of mechanical engineering and civil engineering, to electronics, electrical, earth sciences, climate, agriculture, water resource, mathematical sciences and computer sciences. Specific topics covered include minimax probability machine regression, stochastic finite element method, relevance vector machine, logistic regression, Monte Carlo simulations, random matrix, Gaussian process regression, Kalman filter, stochastic optimization, maximum likelihood, Bayesian inference, Bayesian update, kriging, copula-statistical models, and more. - Explains the application of advanced probabilistic models encompassing multidisciplinary research - Applies probabilistic modeling to emerging areas in engineering - Provides an interdisciplinary approach to probabilistic models and their applications, thus solving a wide range of practical problems
| Author | : Turab Lookman |
| Publisher | : Springer |
| Total Pages | : 316 |
| Release | : 2015-12-12 |
| Genre | : Technology & Engineering |
| ISBN | : 331923871X |
This book deals with an information-driven approach to plan materials discovery and design, iterative learning. The authors present contrasting but complementary approaches, such as those based on high throughput calculations, combinatorial experiments or data driven discovery, together with machine-learning methods. Similarly, statistical methods successfully applied in other fields, such as biosciences, are presented. The content spans from materials science to information science to reflect the cross-disciplinary nature of the field. A perspective is presented that offers a paradigm (codesign loop for materials design) to involve iteratively learning from experiments and calculations to develop materials with optimum properties. Such a loop requires the elements of incorporating domain materials knowledge, a database of descriptors (the genes), a surrogate or statistical model developed to predict a given property with uncertainties, performing adaptive experimental design to guide the next experiment or calculation and aspects of high throughput calculations as well as experiments. The book is about manufacturing with the aim to halving the time to discover and design new materials. Accelerating discovery relies on using large databases, computation, and mathematics in the material sciences in a manner similar to the way used to in the Human Genome Initiative. Novel approaches are therefore called to explore the enormous phase space presented by complex materials and processes. To achieve the desired performance gains, a predictive capability is needed to guide experiments and computations in the most fruitful directions by reducing not successful trials. Despite advances in computation and experimental techniques, generating vast arrays of data; without a clear way of linkage to models, the full value of data driven discovery cannot be realized. Hence, along with experimental, theoretical and computational materials science, we need to add a “fourth leg’’ to our toolkit to make the “Materials Genome'' a reality, the science of Materials Informatics.
