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Mathematics | Optimal Design and Related Areas in Optimization and Statistics

Optimal Design and Related Areas in Optimization and Statistics

Pronzato, Luc, Zhigljavsky, Anatoly (Eds.)

2009

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  • Devoted to applications of the optimal design theory in optimization and statistics
  • Provides comprehensive surveys written by leading generalists
  • Each chapter reviews, analyzes, and extends the statistical literature with rigor and clarity
  • Establishes links between optimization and various areas in experimental design and statistics, including optimal experimental design, majorization and stochastic ordering, algebraic statistics, Bayesian networks, and nonlinear regression
  • Uncovers new applications of optimization to experimental design and statistics
  • Develops new optimization techniques based on ideas from experimental design and statistics
  • Acknowledges the work and influence of statistics scholar Henry P. Wynn

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.

Content Level » Research

Keywords » Bayesian networks - SOIA - algebraic statistics - algorithms - gradient-type algorithms - linear optimization - optimal design theory - optimization

Related subjects » Applications - Computational Science & Engineering - Mathematics - Probability Theory and Stochastic Processes - Statistics - Theoretical Computer Science

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: 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.

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