Interpolation and Extrapolation Optimal Designs V1
Interpolation and Extrapolation Optimal Designs V1

Author: Giorgio Celant

Publisher: John Wiley & Sons

Published: 2016-03-31

Total Pages: 254

ISBN-13: 111929228X

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This book is the first of a series which focuses on the interpolation and extrapolation of optimal designs, an area with significant applications in engineering, physics, chemistry and most experimental fields. In this volume, the authors emphasize the importance of problems associated with the construction of design. After a brief introduction on how the theory of optimal designs meets the theory of the uniform approximation of functions, the authors introduce the basic elements to design planning and link the statistical theory of optimal design and the theory of the uniform approximation of functions. The appendices provide the reader with material to accompany the proofs discussed throughout the book.

Interpolation and Extrapolation Optimal Designs 2
Interpolation and Extrapolation Optimal Designs 2

Author: Giorgio Celant

Publisher: John Wiley & Sons

Published: 2017-04-11

Total Pages: 322

ISBN-13: 1119422361

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This book considers various extensions of the topics treated in the first volume of this series, in relation to the class of models and the type of criterion for optimality. The regressors are supposed to belong to a generic finite dimensional Haar linear space, which substitutes for the classical polynomial case. The estimation pertains to a general linear form of the coefficients of the model, extending the interpolation and extrapolation framework; the errors in the model may be correlated, and the model may be heteroscedastic. Non-linear models, as well as multivariate ones, are briefly discussed. The book focuses to a large extent on criteria for optimality, and an entire chapter presents algorithms leading to optimal designs in multivariate models. Elfving’s theory and the theorem of equivalence are presented extensively. The volume presents an account of the theory of the approximation of real valued functions, which makes it self-consistent.

PROBABILITY AND STATISTICS - Volume III
PROBABILITY AND STATISTICS - Volume III

Author: Reinhard Viertl

Publisher: EOLSS Publications

Published: 2009-06-11

Total Pages: 278

ISBN-13: 1848260547

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Probability and Statistics theme is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme with contributions from distinguished experts in the field, discusses Probability and Statistics. Probability is a standard mathematical concept to describe stochastic uncertainty. Probability and Statistics can be considered as the two sides of a coin. They consist of methods for modeling uncertainty and measuring real phenomena. Today many important political, health, and economic decisions are based on statistics. This theme is structured in five main topics: Probability and Statistics; Probability Theory; Stochastic Processes and Random Fields; Probabilistic Models and Methods; Foundations of Statistics, which are then expanded into multiple subtopics, each as a chapter. These three volumes are aimed at the following five major target audiences: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs.

Computer Aided Optimum Design of Structures III
Computer Aided Optimum Design of Structures III

Author: Santiago Hernández

Publisher:

Published: 1993

Total Pages: 700

ISBN-13:

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Examines the new research on optimization taking place within the scientific community. Emphasis is placed on the numerous applications of the technique in industry for a variety of design problems in fields as diverse as offshore, mechanical, civil and aerospace engineering.

Bayesian Estimation and Experimental Design in Linear Regression Models
Bayesian Estimation and Experimental Design in Linear Regression Models

Author: Jürgen Pilz

Publisher:

Published: 1991-07-09

Total Pages: 316

ISBN-13:

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Presents a clear treatment of the design and analysis of linear regression experiments in the presence of prior knowledge about the model parameters. Develops a unified approach to estimation and design; provides a Bayesian alternative to the least squares estimator; and indicates methods for the construction of optimal designs for the Bayes estimator. Material is also applicable to some well-known estimators using prior knowledge that is not available in the form of a prior distribution for the model parameters; such as mixed linear, minimax linear and ridge-type estimators.