عنوان

Theory and application of uniform experimental designs /

(Number (ISBN

9789811320415

(Number (ISBN

9789811320422

(Number (ISBN

9811320411

(Number (ISBN

981132042X

Erroneous ISBN

9789811320408

Erroneous ISBN

9811320403

Title Proper

Theory and application of uniform experimental designs /

General Material Designation

[Book]

First Statement of Responsibility

Kai-Tai Fang, Min-Qian Liu, Hong Qin, Yong-Dao Zhou.

Place of Publication, Distribution, etc.

Singapore :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

2018.

Specific Material Designation and Extent of Item

1 online resource (xvi, 300 pages) :

Other Physical Details

illustrations (some color)

Series Title

Lecture notes in statistics,

Volume Designation

volume 221

ISSN of Series

0930-0325 ;

Text of Note

Includes bibliographical references and index.

Text of Note

Intro; Foreword; Preface; References; Contents; 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.

Text of Note

1.5 Implementation of Uniform Designs for Multifactor Experiments1.6 Applications of the Uniform Design; 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 L2-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.

Text of Note

2.6.1 Lower Bounds of the Centered L2-Discrepancy2.6.2 Lower Bounds of the Wrap-around L2-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; 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.

Text of Note

3.3.2 The Leave-One-Out glpm3.3.3 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; 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.

Text of Note

4.3.1 Quadratic Forms of Discrepancies4.3.2 Complementary Design Theory; 4.3.3 Optimal Frequency Vector; 4.3.4 Integer Programming Problem Method; 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; References.

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Text of Note

The book provides necessary knowledge for readers interested in developing the theory of uniform experimental design. It discusses measures of uniformity, various construction methods of uniform designs, modeling techniques, design and modeling for experiments with mixtures, and the usefulness of the uniformity in block, factorial and supersaturated designs. Experimental design is an important branch of statistics with a long history, and is extremely useful in multi-factor experiments. Involving rich methodologies and various designs, it has played a key role in industry, technology, sciences and various other fields. A design that chooses experimental points uniformly scattered on the domain is known as uniform experimental design, and uniform experimental design can be regarded as a fractional factorial design with model uncertainty, a space-filling design for computer experiments, a robust design against the model specification, and a supersaturated design and can be applied to experiments with mixtures.

Source for Acquisition/Subscription Address

Springer Nature

Stock Number

com.springer.onix.9789811320415

Title

Theory and application of uniform experimental designs.

International Standard Book Number

9789811320408

Experimental design.

Experimental design.

Mathematics-- Probability & Statistics-- General.

Probability & statistics.

MAT029000

PBT

PBT

Number

Edition

Class number

Fang, Kaitai

Liu, Min-Qian

Qin, Hong

Zhou, Yong-Dao

Date of Transaction

20200823225954.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y