Patil / Gore / Taillie Composite Sampling

A Novel Method to Accomplish Observational Economy in Environmental Studies
1. Auflage 2010
ISBN: 978-1-4419-7628-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 4, 275 Seiten

Reihe: Environmental and Ecological Statistics

Sampling consists of selection, acquisition, and quantification of a part of the population. While selection and acquisition apply to physical sampling units of the population, quantification pertains only to the variable of interest, which is a particular characteristic of the sampling units. A sampling procedure is expected to provide a sample that is representative with respect to some specified criteria. Composite sampling, under idealized conditions, incurs no loss of information for estimating the population means. But an important limitation to the method has been the loss of information on individual sample values, such as, the extremely large value. In many of the situations where individual sample values are of interest or concern, composite sampling methods can be suitably modified to retrieve the information on individual sample values that may be lost due to compositing. This book presents statistical solutions to issues that arise in the context of applications of composite sampling.

Autoren/Hrsg.

Patil, Ganapati P.

Gore, Sharad D.

Taillie, Charles

Inhaltsverzeichnis

1;Acknowledgements;6
2;Contents;7
3;1 Introduction;12
4;2 Classifying Individual Samples into Oneof Two Categories ;19
4.1;2.1 Introduction;19
4.2;2.2 Presence/Absence Measurements;21
4.2.1;2.2.1 Exhaustive Retesting;22
4.2.2;2.2.2 Sequential Retesting;25
4.2.3;2.2.3 Binary Split Retesting;28
4.2.4;2.2.4 Curtailed Exhaustive Retesting;33
4.2.5;2.2.5 Curtailed Sequential Retesting;37
4.2.6;2.2.6 Curtailed Binary Split Retesting;41
4.2.7;2.2.7 Entropy-Based Retesting;43
4.2.8;2.2.8 Exhaustive Retesting in the Presence of Classification Errors;48
4.2.9;2.2.9 Other Costs;50
4.3;2.3 Continuous Response Variables;51
4.3.1;2.3.1 Quantitatively Curtailed Exhaustive Retesting;55
4.3.2;2.3.2 Binary Split Retesting;56
4.3.3;2.3.3 Entropy-Based Retesting;59
4.4;2.4 Cost Analysis of Composite Sampling for Classification;59
4.4.1;2.4.1 Introduction;59
4.4.2;2.4.2 General Cost Expression;59
4.4.3;2.4.3 Effect of False Positives and False Negatives on Composite Sample Classification;60
4.4.4;2.4.4 Presence/Absence Measurements;61
4.4.5;2.4.5 Continuous Measurements;63
5;3 Identifying Extremely Large Observations;64
5.1;3.1 Introduction;64
5.2;3.2 Prediction of the Sample Maximum;65
5.3;3.3 The Sweep-Out Method to Identify the Sample Maximum;67
5.4;3.4 Extensive Search of Extreme Values;68
5.5;3.5 Application;69
5.6;3.6 Two-Way Composite Sampling Design;77
5.7;3.7 Illustrative Example;79
5.8;3.8 Analysis of Composite Sampling Data Using the Principle of Maximum Entropy;85
5.8.1;3.8.1 Introduction;85
5.8.2;3.8.2 Modeling Composite Sampling Using the Principle of Maximum Entropy;86
5.8.3;3.8.3 When Is the Maximum Entropy Model Reasonable in Practice?;87
6;4 Estimating Prevalence of a Trait;89
6.1;4.1 Introduction;89
6.2;4.2 The Maximum Likelihood Estimator;90
6.3;4.3 Alternative Estimators;92
6.4;4.4 Comparison Between p and p;93
6.5;4.5 Estimation of Prevalence in Presence of Measurement Error;93
7;5 A Bayesian Approach to the Classification Problem ;95
7.1;5.1 Introduction;95
7.2;5.2 Bayesian Updating of p;98
7.3;5.3 Minimization of the Expected Relative Cost;101
7.4;5.4 Discussion;103
8;6 Inference on Mean and Variance;105
8.1;6.1 Introduction;105
8.2;6.2 Notation and Basic Results;106
8.2.1;6.2.1 Notation;106
8.2.2;6.2.2 Basic Results;107
8.3;6.3 Estimation Without Measurement Error;109
8.4;6.4 Estimation in the Presence of Measurement Error;111
8.5;6.5 Maintaining Precision While Reducing Cost;112
8.6;6.6 Estimation of 2x and 2;113
8.7;6.7 Estimation of Population Variance;114
8.8;6.8 Confidence Interval for the Population Mean;117
8.9;6.9 Tests of Hypotheses in the Population Mean;118
8.9.1;6.9.1 One-Sample Tests;118
8.9.2;6.9.2 Two-Sample Tests;119
8.10;6.10 Applications;120
8.10.1;6.10.1 Comparison of Arithmetic Averages of Soil pH Values with the pH Values of Composite Samples;120
8.10.2;6.10.2 Comparison of Random and Composite Sampling Methods for the Estimation of Fat Contents of Bulk Milk Supplies;120
8.10.3;6.10.3 Optimization of Sampling for the Determination of Mean Radium-226 Concentration in Surface Soil;121
9;7 Composite Sampling with Random Weights;123
9.1;7.1 Introduction;123
9.2;7.2 Expected Value, Variance, and Covariance of Bilinear Random Forms;124
9.3;7.3 Models for the Weights;126
9.3.1;7.3.1 Assumptions on the First Two Moments;127
9.3.2;7.3.2 Distributional Assumptions;127
9.4;7.4 The Model for Composite Sample Measurements;129
9.4.1;7.4.1 Subsampling a Composite Sample;129
9.4.2;7.4.2 Several Composite Samples;132
9.4.3;7.4.3 Subsampling of Several Composite Samples;133
9.4.4;7.4.4 Measurement Error;134
9.5;7.5 Applications;136
9.5.1;7.5.1 Sampling Frequency and Comparison of Graband Composite Sampling Programs for Effluents;136
9.5.2;7.5.2 Theoretical Comparison of Grab and Composite Sampling Programs;136
9.5.3;7.5.3 Grab vs. Composite Sampling: A Primer for the Manager and Engineer;137
9.5.4;7.5.4 Composite Samples Overestimate Waste Loads;137
9.5.5;7.5.5 Composite Samples for Foliar Analysis;140
9.5.6;7.5.6 Lateral Variability of Forest Floor Properties Under Second-Growth Douglas-Fir Stands and the Usefulness of Composite SamplingTechniques;141
10;8 A Linear Model for Estimation with Composite Sample Data;143
10.1;8.1 Introduction;143
10.2;8.2 Motivation for a Unified Model;144
10.3;8.3 The Model;145
10.4;8.4 Discussion of the Assumptions;147
10.4.1;8.4.1 The Structural/Sampling Submodel;147
10.4.2;8.4.2 The Compositing/Subsampling Submodel;148
10.4.3;8.4.3 The Structure of the Matrices W, MW, and W;148
10.5;8.5 Moments of x and y;154
10.6;8.6 Complex Sampling Schemes Before Compositing;154
10.6.1;8.6.1 Segmented Populations;155
10.6.2;8.6.2 Estimating the Mean in Segmented Populations;155
10.6.3;8.6.3 Estimating Variance Components in Segmented Populations;158
10.7;8.7 Estimating the Effect of a Binary Factor;161
10.7.1;8.7.1 Fully Segregated Composites;165
10.7.2;8.7.2 Fully Confounded Composites;169
10.8;8.8 Elementary Matrices and Kronecker Products;172
10.8.1;8.8.1 Decomposition of Block Matrices;173
10.9;8.9 Expectation and Dispersion Matrix When Both W and x Are Random;176
10.9.1;8.9.1 The Expectation of Wx;176
10.9.2;8.9.2 Variance/Covariance Matrix of Wx;180
11;9 Composite Sampling for Site Characterization and Cleanup Evaluation;182
11.1;9.1 Data Quality Objectives;182
11.2;9.2 Optimal Composite Designs;185
11.2.1;9.2.1 Cost of a Sampling Program;186
11.2.2;9.2.2 Optimal Allocation of Resources;186
11.2.3;9.2.3 Power of a Test and Determination of Sample Size;187
11.2.4;9.2.4 Algorithms for Determination of Sample Size;188
12;10 Spatial Structures of Site Characteristics and Composite Sampling;190
12.1;10.1 Introduction;190
12.2;10.2 Models for Spatial Processes;190
12.2.1;10.2.1 Composite Sampling;194
12.3;10.3 Application to Two Superfund Sites;197
12.3.1;10.3.1 The Two Sites;197
12.3.2;10.3.2 Methods;198
12.3.3;10.3.3 Results;199
12.3.4;10.3.4 Discussion;202
12.4;10.4 Compositing by Spatial Contiguity;205
12.4.1;10.4.1 Introduction;205
12.4.2;10.4.2 Retesting Strategies;206
12.4.3;10.4.3 Composite Sample-Forming Schemes;207
12.5;10.5 Compositing of Ranked Set Samples;208
12.5.1;10.5.1 Ranked Set Sampling;208
12.5.2;10.5.2 Relative Precision of the RSS Estimatorof a Population Mean Relative to Its SRS Estimator;211
12.5.3;10.5.3 Unequal Allocation of Sample Sizes;212
12.5.4;10.5.4 Formation of Homogeneous Composite Samples;213
13;11 Composite Sampling of Soils and Sediments ;215
13.1;11.1 Detection of Contamination;215
13.1.1;11.1.1 Detecting PCB Spills;215
13.1.2;11.1.2 Compositing Strategy for Analysis of Samples;217
13.2;11.2 Estimation of the Average Level of Contamination;219
13.2.1;11.2.1 Estimation of the Average PCB Concentrationon the Spill Area;219
13.2.2;11.2.2 Onsite Surface Soil Sampling for PCBat the Armagh Site;220
13.2.3;11.2.3 The Armagh Site;221
13.2.4;11.2.4 Simulating Composite Samples;224
13.2.5;11.2.5 Locating Individual Samples with High PCB Concentrations;227
13.3;11.3 Estimation of Trace Metal Storage in Lake St. Clair Post-settlement Sediments Using Composite Samples;228
14;12 Composite Sampling of Liquids and Fluids;232
14.1;12.1 Comparison of Random and Composite Sampling Methodsfor the Estimation of Fat Content of Bulk Milk Supplies;232
14.1.1;12.1.1 Experiment;232
14.1.2;12.1.2 Estimation Methods;233
14.1.3;12.1.3 Results;233
14.1.4;12.1.4 Composite Compared with Yield-Weighted Estimate of Fat Percentage;234
14.2;12.2 Composite Sampling of Highway Runoff;234
14.3;12.3 Composite Samples Overestimate Waste Loads;237
15;13 Composite Sampling and Indoor Air Pollution ;240
15.1;13.1 Household Dust Samples;240
16;14 Composite Sampling and Bioaccumulation ;243
16.1;14.1 Example: National Human Adipose Tissue Survey;245
16.2;14.2 Results from the Analysis of 1987 NHATS Data;245
17;Glossary and Terminology;247
18;Bibliography;253
19;Index;271