Optimal design and related areas in optimization and statistics

✍ Scribed by Pronzato L., Zhigljavsky A. (eds.)

• Publisher: Springer
• Year: 2008
• Tongue: English
• Leaves: 241
• Series: Springer Optimization and Its Applications
• Category: Library

✦ Synopsis

This edited volume, dedicated to Henry P. Wynn, reflects his broad range of research interests, focusing in particular on the applications of optimal design theory in optimization and statistics. It covers algorithms for constructing optimal experimental designs, general gradient-type algorithms for convex optimization, majorization and stochastic ordering, algebraic statistics, Bayesian networks and nonlinear regression. Written by leading specialists in the field, each chapter contains a survey of the existing literature along with substantial new material. This work will appeal to both the specialist and the non-expert in the areas covered. By attracting the attention of experts in optimization to important interconnected areas, it should help stimulate further research with a potential impact on applications.

✦ Table of Contents

Cover......Page 1
Springer Optimization and Its Applications VOLUME 28......Page 3
Optimal Design and Related Areas in Optimization and Statistics......Page 4
9780387799353......Page 5
Dedication......Page 6
Preface......Page 10
List of Contributors......Page 12
Contents......Page 14
1.2 Optimal Design and an Optimization Problem......Page 18
1.3 Derivatives and Optimality Conditions......Page 19
1.4 Algorithms......Page 20
1.6 Simultaneous Approach to Optimal Weight and Support Point Determination......Page 26
References......Page 28
2.1 Introduction......Page 30
2.2 Renormalized Version of Gradient Algorithms......Page 31
2.3 A Multiplicative Algorithm for Optimal Design......Page 33
2.4 Constructing Optimality Criteria which Correspond to a Given Gradient Algorithm......Page 35
2.5 Optimum Design Gives the Worst Rate of Convergence......Page 36
2.6 Some Special Cases......Page 37
2.7 The Steepest-Descent Algorithm with Relaxation......Page 40
2.8 Square-Root Algorithm......Page 47
2.9 A-Optimality......Page 49
2.10 a-Root Algorithm and Comparisons......Page 50
References......Page 53
3.1 Introduction......Page 56
3.2 The Optimum s-Gradient Algorithm for the Minimization of a Quadratic Function......Page 57
3.3 Asymptotic Behaviour of the Optimum s-Gradient Algorithm in \mathbb{R}^d......Page 69
3.4 The Optimum 2-Gradient Algorithm in \mathbb{R}^d......Page 72
3.5 Switching Algorithms......Page 83
References......Page 96
4.1 Introduction......Page 98
4.2 Dependence Orderings for Two Nominal Variables......Page 100
4.3 Inter-Raters Agreement for Categorical Classifications......Page 107
4.4 Conclusions and Further Research......Page 111
References......Page 112
5.1 Introduction......Page 114
5.2 Background......Page 115
5.3 Generalized Confounding and Polynomial Algebra......Page 119
5.4 Models and Monomials......Page 130
5.5 Indicator Function for Complex Coded Designs......Page 135
5.6 Indicator Function vs. Grobner Basis......Page 138
5.7 Mixture Designs......Page 143
5.8 Conclusions......Page 147
References......Page 148
6.1 The Algebra of Probability Trees......Page 150
6.2 Manifest Probabilities and Solution Spaces......Page 154
6.3 Expressing Causal Effects Through Algebra......Page 156
6.4 From Models to Causal ACTs to Analysis......Page 159
6.5 Equivalent Causal ACTs......Page 164
6.6 Conclusions......Page 168
References......Page 171
7.1 Bayes Nets and Projections......Page 172
7.2 Time Series: Stochastic Realization and Conditional Independence......Page 177
7.3 LCO/LCI Time Series......Page 180
7.4 TDAG as Generalized Time......Page 182
References......Page 183
8.1 Introduction......Page 184
8.2 The Convergence of the Design Sequence to a Design Measure......Page 188
8.3 Consistency of Estimators......Page 193
8.4 On the Geometry of the Model Under the Design Measure ?......Page 196
8.5 The Regular Asymptotic Normality of h(\hat{\theta}^N)......Page 199
8.6 Estimation of a Multidimensional Function H(θ)......Page 203
References......Page 207
9.1 Introduction......Page 210
9.2 Main Results......Page 213
9.3 Auxiliary Assertions......Page 224
9.4 Proofs......Page 232
References......Page 234
Index......Page 240