Optimal Design and Related Areas in Optimization and Statistics / Edition 1

by Luc Pronzato, Anatoly Zhigljavsky

Overview

The present volume is a collective monograph devoted to applications of the optimal design theory in optimization and statistics. The chapters reffect 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 reffect the wide spectrum of Henry’s research - terests. Algorithms for constructing optimal designs are discussed in Chap. 1, where Henry’s contribution to the field is acknowledged. Steepest-ascent - gorithms used to construct optimal designs are very much related to general gradient algorithms for convexoptimization. Inthelasttenyears,asignificant 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 sh- 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.

Product Details

ISBN-13:	9781441927323
Publisher:	Springer New York
Publication date:	09/08/2011
Series:	Springer Optimization and Its Applications , #28
Edition description:	2009
Pages:	224
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

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: Shastic Realizations and Projections.- Asymptotic Normality of Nonlinear Least Squares under Singular Experimental Designs.- Robust Estimators in Non-linear Regression Models with Long-Range Dependence.