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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.
Book Synopsis Sequential Analysis and Optimal Design by : Herman Chernoff
Download or read book Sequential Analysis and Optimal Design written by Herman Chernoff and published by SIAM. This book was released on 1972-01-31 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Sequential Analysis and Optimal Design by : Herman Chernoff
Download or read book Sequential Analysis and Optimal Design written by Herman Chernoff and published by SIAM. This book was released on 1972-01-01 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Optimal Design by : S. Silvey
Download or read book Optimal Design written by S. Silvey and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimum Design 2000 by : Anthony Atkinson
Download or read book Optimum Design 2000 written by Anthony Atkinson and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimum Design 2000
The global approach to nonlinear renewal theory is integrated with the author's own local approach. Both the theory and its applications are placed in perspective by including a discussion of the linear renewal theorem and its applications to the sequential probability ratio test. Applications to repeated significance tests, to tests with power one, and to sequential estimation are also included. The monograph is self-contained for readers with a working knowledge of measure-theoretic probability and intermediate statistical theory.
Book Synopsis Nonlinear Renewal Theory in Sequential Analysis by : Michael Woodroofe
Download or read book Nonlinear Renewal Theory in Sequential Analysis written by Michael Woodroofe and published by SIAM. This book was released on 1982-01-01 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The global approach to nonlinear renewal theory is integrated with the author's own local approach. Both the theory and its applications are placed in perspective by including a discussion of the linear renewal theorem and its applications to the sequential probability ratio test. Applications to repeated significance tests, to tests with power one, and to sequential estimation are also included. The monograph is self-contained for readers with a working knowledge of measure-theoretic probability and intermediate statistical theory.
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
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
Sequential analysis refers to the body of statistical theory and methods where the sample size may depend in a random manner on the accumulating data. A formal theory in which optimal tests are derived for simple statistical hypotheses in such a framework was developed by Abraham Wald in the early 1
Book Synopsis Handbook of Sequential Analysis by : B.K. Ghosh
Download or read book Handbook of Sequential Analysis written by B.K. Ghosh and published by CRC Press. This book was released on 1991-04-24 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sequential analysis refers to the body of statistical theory and methods where the sample size may depend in a random manner on the accumulating data. A formal theory in which optimal tests are derived for simple statistical hypotheses in such a framework was developed by Abraham Wald in the early 1
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
Book Synopsis Optimal Experimental Design with R by : Dieter Rasch
Download or read book Optimal Experimental Design with R written by Dieter Rasch and published by CRC Press. This book was released on 2011-05-18 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
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.
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.
This book includes many of the papers presented at the 6th International workshop on Model Oriented Data Analysis held in June 2001. This series began in March 1987 with a meeting on the Wartburg near Eisenach (at that time in the GDR). The next four meetings were in 1990 (St Kyrik monastery, Bulgaria), 1992 (Petrodvorets, St Petersburg, Russia), 1995 (Spetses, Greece) and 1998 (Marseilles, France). Initially the main purpose of these workshops was to bring together leading scientists from 'Eastern' and 'Western' Europe for the exchange of ideas in theoretical and applied statistics, with special emphasis on experimental design. Now that the sep aration between East and West is much less rigid, this exchange has, in principle, become much easier. However, it is still important to provide opportunities for this interaction. MODA meetings are celebrated for their friendly atmosphere. Indeed, dis cussions between young and senior scientists at these meetings have resulted in several fruitful long-term collaborations. This intellectually stimulating atmosphere is achieved by limiting the number of participants to around eighty, by the choice of a location in which communal living is encour aged and, of course, through the careful scientific direction provided by the Programme Committee. It is a tradition of these meetings to provide low cost accommodation, low fees and financial support for the travel of young and Eastern participants. This is only possible through the help of sponsors and outside financial support was again important for the success of the meeting.
Book Synopsis MODA 6 - Advances in Model-Oriented Design and Analysis by : Anthony C. Atkinson
Download or read book MODA 6 - Advances in Model-Oriented Design and Analysis written by Anthony C. Atkinson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes many of the papers presented at the 6th International workshop on Model Oriented Data Analysis held in June 2001. This series began in March 1987 with a meeting on the Wartburg near Eisenach (at that time in the GDR). The next four meetings were in 1990 (St Kyrik monastery, Bulgaria), 1992 (Petrodvorets, St Petersburg, Russia), 1995 (Spetses, Greece) and 1998 (Marseilles, France). Initially the main purpose of these workshops was to bring together leading scientists from 'Eastern' and 'Western' Europe for the exchange of ideas in theoretical and applied statistics, with special emphasis on experimental design. Now that the sep aration between East and West is much less rigid, this exchange has, in principle, become much easier. However, it is still important to provide opportunities for this interaction. MODA meetings are celebrated for their friendly atmosphere. Indeed, dis cussions between young and senior scientists at these meetings have resulted in several fruitful long-term collaborations. This intellectually stimulating atmosphere is achieved by limiting the number of participants to around eighty, by the choice of a location in which communal living is encour aged and, of course, through the careful scientific direction provided by the Programme Committee. It is a tradition of these meetings to provide low cost accommodation, low fees and financial support for the travel of young and Eastern participants. This is only possible through the help of sponsors and outside financial support was again important for the success of the meeting.
