Ebook: Functional Approach to Optimal Experimental Design
Author: Viatcheslav B. Melas (auth.)
- Tags: Statistical Theory and Methods, Statistics for Engineering Physics Computer Science Chemistry & Geosciences, Statistics for Life Sciences Medicine Health Sciences, Simulation and Modeling, Optimization
- Series: Lecture Notes in Statistics 184
- Year: 2006
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
The book presents a novel approach for studying optimal experimental designs. The functional approach consists of representing support points of the designs by Taylor series. It is thoroughly explained for many linear and nonlinear regression models popular in practice including polynomial, trigonometrical, rational, and exponential models. Using the tables of coefficients of these series included in the book, a reader can construct optimal designs for specific models by hand.
The book is suitable for researchers in statistics and especially in experimental design theory as well as to students and practitioners with a good mathematical background.
Viatcheslav B. Melas is Professor of Statistics and Numerical Analysis at the St. Petersburg State University and the author of more than one hundred scientific articles and four books. He is an Associate Editor of the Journal of Statistical Planning and Inference and Co-Chair of the organizing committee of the 1st–5th St. Petersburg Workshops on Simulation (1994, 1996, 1998, 2001 and 2005).
The book presents a novel approach for studying optimal experimental designs. The functional approach consists of representing support points of the designs by Taylor series. It is thoroughly explained for many linear and nonlinear regression models popular in practice including polynomial, trigonometrical, rational, and exponential models. Using the tables of coefficients of these series included in the book, a reader can construct optimal designs for specific models by hand.
The book is suitable for researchers in statistics and especially in experimental design theory as well as to students and practitioners with a good mathematical background.
Viatcheslav B. Melas is Professor of Statistics and Numerical Analysis at the St. Petersburg State University and the author of more than one hundred scientific articles and four books. He is an Associate Editor of the Journal of Statistical Planning and Inference and Co-Chair of the organizing committee of the 1st–5th St. Petersburg Workshops on Simulation (1994, 1996, 1998, 2001 and 2005).
The book presents a novel approach for studying optimal experimental designs. The functional approach consists of representing support points of the designs by Taylor series. It is thoroughly explained for many linear and nonlinear regression models popular in practice including polynomial, trigonometrical, rational, and exponential models. Using the tables of coefficients of these series included in the book, a reader can construct optimal designs for specific models by hand.
The book is suitable for researchers in statistics and especially in experimental design theory as well as to students and practitioners with a good mathematical background.
Viatcheslav B. Melas is Professor of Statistics and Numerical Analysis at the St. Petersburg State University and the author of more than one hundred scientific articles and four books. He is an Associate Editor of the Journal of Statistical Planning and Inference and Co-Chair of the organizing committee of the 1st–5th St. Petersburg Workshops on Simulation (1994, 1996, 1998, 2001 and 2005).
Content:
Front Matter....Pages i-ix
Introduction....Pages 1-4
Fundamentals of the Optimal Experimental Design....Pages 5-21
The Functional Approach....Pages 23-70
Polynomial Models....Pages 71-133
Trigonometrical Models....Pages 135-195
D-Optimal Designs for Rational Models....Pages 197-216
D-Optimal Designs for Exponential Models....Pages 217-230
E- and c-Optimal Designs....Pages 231-271
The Monod Model....Pages 273-316
Back Matter....Pages 317-333
The book presents a novel approach for studying optimal experimental designs. The functional approach consists of representing support points of the designs by Taylor series. It is thoroughly explained for many linear and nonlinear regression models popular in practice including polynomial, trigonometrical, rational, and exponential models. Using the tables of coefficients of these series included in the book, a reader can construct optimal designs for specific models by hand.
The book is suitable for researchers in statistics and especially in experimental design theory as well as to students and practitioners with a good mathematical background.
Viatcheslav B. Melas is Professor of Statistics and Numerical Analysis at the St. Petersburg State University and the author of more than one hundred scientific articles and four books. He is an Associate Editor of the Journal of Statistical Planning and Inference and Co-Chair of the organizing committee of the 1st–5th St. Petersburg Workshops on Simulation (1994, 1996, 1998, 2001 and 2005).
Content:
Front Matter....Pages i-ix
Introduction....Pages 1-4
Fundamentals of the Optimal Experimental Design....Pages 5-21
The Functional Approach....Pages 23-70
Polynomial Models....Pages 71-133
Trigonometrical Models....Pages 135-195
D-Optimal Designs for Rational Models....Pages 197-216
D-Optimal Designs for Exponential Models....Pages 217-230
E- and c-Optimal Designs....Pages 231-271
The Monod Model....Pages 273-316
Back Matter....Pages 317-333
....