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Multidimensional Balanced Error Sampling

Daniel DAVIS,Catherine GOYET
Collection
Études
Editeur
Presses Universitaires de Perpignan
Date de publication
25 septembre 2025
Résumé
Prepare to transform your understanding of sampling and enrich your research work with innovative and effective tools. Whether you are a researcher, student, or curious individual, this book allows you to delve into an essential work that revolutionizes multidimensional sampling of the environment.Explore the fundamental concepts, theorems, methods, and algorithms necessary for a practical approach to first- order multidimensional balanced error sampling, while taking into account various constraints such as the number of samples, study area (which may be a surface or a volume), as well as the expected variability of the analyzed properties.With a rigorous and detailed mathematical approach, this work applies to an infinite number of dimensions, thus offering limitless ... Lire la suite
FORMAT
Livre broché
30.00 €
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Actuellement Indisponible
Crédit
Date de première publication du titre 25 septembre 2025
ISBN 9782354124946
EAN-13 9782354124946
Référence 129388-58
Nombre de pages de contenu principal 143
Format 16 x 24 x 1 cm
Poids 290 g

INTRODUCTION 1


CHAPTER 1. Essential mathematical concepts 5
1.0. Overview 5
1.1. Mathematical Basis 5
1.2. First order sample error, sample data variability sample spacing
and the Sample Error Theorem 12
1.3. Maximum error of cells for a tessellation given a positive variability
bound for its data cells 26


CHAPTER 2. Extending 1-D results to 2-D. 35
2.0. The development of semi-balanced tessellations in any dimension 35
2.1. Extending one-dimensional results to two dimensions 40
2.2. Symmetries of coordinates 65


CHAPTER 3. Extending 2D Results to K dimensions 67
3.0. Extending to K dimensions 67
3.1. Properties of the transformation ( ) :[ , ] [ , ] K F x a b ? a b 88
3.2. The semi-balanced property of the transformed K-cells 96

CHAPTER 4. Practical methodology 99
4.0. Introduction to practical multidimensional balanced error sampling 99
4.1. Basic summary of mathematical concepts and results 100
4.2. Practical Methodology 108
4.3. Determining a variability bound from sample data sets 110
4.4. Analyzing maximum sample error versus sample size 116
4.5. Determining a semi-balanced tessellation with M 2-cells given the
variability Bound B(x) 119
4.6. Interpolation using the semi-balanced pattern of points produced by
the transformation 2 F (x) :[a, b]?[a, b] 125


SUMMARY and CONCLUSIONS 131


REFERENCES 133


EXPANDED TABLE OF CONTENTS 135


INDEX 139

 

Prepare to transform your understanding of sampling and enrich your research work with innovative and effective tools. Whether you are a researcher, student, or curious individual, this book allows you to delve into an essential work that revolutionizes multidimensional sampling of the environment.Explore the fundamental concepts, theorems, methods, and algorithms necessary for a practical approach to first- order multidimensional balanced error sampling, while taking into account various constraints such as the number of samples, study area (which may be a surface or a volume), as well as the expected variability of the analyzed properties.With a rigorous and detailed mathematical approach, this work applies to an infinite number of dimensions, thus offering limitless practical application perspectives. The results presented here illuminate and systematize practices that have often been intuitive until now, paving the way for new sampling design methods suitable for many research fields, particularly in environmental studies.

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