1 Introduction
1.1 Experiments
1.1.1 Examples
1.1.2 Experimental Characteristics
1.1.3 Type of Experiments
1.2 Basic Terminologies Used
1.3 Statistical Models
1.3.1 Factorial Designs and ANOVA Models
1.3.2 Fractional Factorial Designs
1.3.3 Linear Regression Models
1.3.4 Nonparametric Regression Models
1.3.5 Robustness of Regression Models
1.4 Word-Length Pattern: Resolution and Minimum Aberration
1.4.1 Ordering
1.4.2 Defining Relation
1.4.3 Word-Length Pattern and Resolution
1.4.4 Minimum Aberration Criterion and Its Extension
1.5 Implementation of Uniform Designs for Multifactor Experiments
1.6 Applications of the Uniform Design
Exercises
References
2 Uniformity Criteria
2.1 Overall Mean Model
2.2 Star Discrepancy
2.2.1 Definition
2.2.2 Properties
2.3 Generalized L2-Discrepancy
2.3.1 Definition
2.3.2 Centered/_~-Discrepancy
2.3.3 Wrap-around L2-Discrepancy
2.3.4 Some Discussion on CD and WD
2.3.5 Mixture Discrepancy
2.4 Reproducing Kernel for Discrepancies
2.5 Discrepancies for Finite Numbers of Levels
2.5.1 Discrete Discrepancy
2.5.2 Lee Discrepancy
2.6 Lower Bounds of Discrepancies
2.6.1 Lower Bounds of the Centered Lz-Discrepancy
2.6.2 Lower Bounds of the Wrap-around Lz-Discrepancy
2.6.3 Lower Bounds of Mixture Discrepancy
2.6.4 Lower Bounds of Discrete Discrepancy
2.6.5 Lower Bounds of Lee Discrepancy
Exercises
References
3 Construction of Uniform Designs--Deterministic Methods
3.1 Uniform Design Tables
3.1.1 Background of Uniform Design Tables
3.1.2 One-Factor Uniform Designs
3.2 Uniform Designs with Multiple Factors
3.2.1 Complexity of the Construction
3.2.2 Remarks
3.3 Good Lattice Point Method and Its Modifications
3.3.1 Good Lattice Point Method
3.3.2 The Leave-One-Out glpm
3.3.3 Good Lattice Point with Power Generator
3.4 The Cutting Method
3.5 Linear Level Permutation Method
3.6 Combinatorial Construction Methods
3.6.1 Connection Between Uniform Designs and Uniformly Resolvable Designs
3.6.2 Construction Approaches via Combinatorics
3.6.3 Construction Approach via Saturated Orthogonal Arrays
3.6.4 Further Results
Exercises
References
4 Construction of Uniform Designs--Algorithmic Optimization Methods
4.1 Numerical Search for Uniform Designs
4.2 Threshold-Accepting Method
4.3 Construction Method Based on Quadratic Form
4.3.1 Quadratic Forms of Discrepancies
4.3.2 Complementary Design Theory
4.3.3 Optimal Frequency Vector
4.3.4 Integer Programming Problem Method
Exercises
References
5 Modeling Techniques
5.1 Basis Functions
5.1.1 Polynomial Regression Models
5.1.2 Spline Basis
5.1.3 Wavelets Basis
5.1.4 Radial Basis Functions
5.1.5 Selection of Variables
5.2 Modeling Techniques: Kriging Models
5.2.1 Models
5.2.2 Estimation
5.2.3 Maximum Likelihood Estimation
5.2.4 Parametric Empirical Kriging
5.2.5 Examples and Discussion
5.3 A Case Study on Environmental Data--Model Selection
Exercises
References
6 Connections Between Uniformity and Other Design Criteria
6.1 Uniformity and Isomorphism
6.2 Uniformity and Orthogonality
6.3 Uniformity and Confounding
6.4 Uniformity and Aberration
6.5 Projection Uniformity and Related Criteria
6.5.1 Projection Discrepancy Pattern and Related Criteria
6.5.2 Uniformity Pattern and Related Criteria
6.6 Majorization Framework
6.6.1 Based on Pairwise Coincidence Vector
6.6.2 Minimum Aberration Majorization
Exercises
References
7 Applications of Uniformity in Other Design Types
7.1 Uniformity in Block Designs
7.1.1 Uniformity in BIBDs
7.1.2 Uniformity in PRIBDs
7.1.3 Uniformity i

方开泰、刘民千、覃红、周永道编的《均匀试验设计的理论和应用(英文版)(精)》讲述了The book provides necessary knowledge for readers interested in developing thetheory of uniform experimental design. It discusses measures of uniformity, variousconstruction methods of uniform designs, modeling techniques, design and modelingfor experiments with mixtures, and the usefulness of the uniformity in block, factorialand supersaturated designs.
Experimental design is an important branch of statistics with a long history, and isextremely useful in multi-factor experiments. Involving rich methodologies and vari-ous designs, it has played a key role in industry, technology, sciences and variousother fields. A design that chooses experimental points uniformly scattered on thedomain is known as uniform experimental design, and uniform experimental designcan be regarded as a fractional factorial design with model uncertainty, a space-fillingdesign for computer experiments, a robust design against the model specificaion, anda supersaturated design and can be applied to experiments with mixtures.