Optimal Design and Related Areas in Optimization and Statistics

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.

Zusammenfassung
The present volume is a collective monograph devoted to applications of the optimal design theory in optimization and statistics. The chapters re?ect the topics discussed at the workshop W-Optimum Design and Related Statistical Issues that took place in Juan-les-Pins, France, in May 2005. The title of the workshop was chosen as a light-hearted celebration of the work of Henry Wynn. It was supported by the Laboratoire I3S (CNRS/Universit´ e de Nice, Sophia Antipolis), to which Henry is a frequent visitor. The topics covered partly re?ect the wide spectrum of Henry's research - terests. Algorithms for constructing optimal designs are discussed in Chap. 1, where Henry's contribution to the ?eld is acknowledged. Steepest-ascent - gorithms used to construct optimal designs are very much related to general gradientalgorithmsforconvexoptimization. Inthelasttenyears,asigni?cant part of Henry's research was devoted to the study of the asymptotic prop- ties of such algorithms. This topic is covered by Chaps. 2 and 3. The work by Alessandra Giovagnoli concentrates on the use of majorization and stoch- tic ordering, and Chap. 4 is a hopeful renewal of their collaboration. One of Henry's major recent interests is what is now called algebraic statistics, the application of computational commutative algebra to statistics, and he was partly responsible for introducing the experimental design sub-area, reviewed in Chap. 5. One other sub-area is the application to Bayesian networks and Chap. 6 covers this, with Chap. 7 being strongly related.

Inhalt
W-Iterations and Ripples Therefrom.- Studying Convergence of Gradient Algorithms Via Optimal Experimental Design Theory.- A Dynamical-System Analysis of the Optimum s-Gradient Algorithm.- Bivariate Dependence Orderings for Unordered Categorical Variables.- Methods in Algebraic Statistics for the Design of Experiments.- The Geometry of Causal Probability Trees that are Algebraically Constrained.- Bayes Nets of Time Series: Stochastic Realizations and Projections.- Asymptotic Normality of Nonlinear Least Squares under Singular Experimental Designs.- Robust Estimators in Non-linear Regression Models with Long-Range Dependence.