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Composite Sampling - A Novel Method to Accomplish Observational Economy in Environmental Studies
von: Ganapati P. Patil, Sharad D. Gore, Charles Taillie
Springer-Verlag, 2010
ISBN: 9781441976284 , 275 Seiten
Format: PDF
Kopierschutz: DRM
Preis: 96,29 EUR
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Composite Sampling - A Novel Method to Accomplish Observational Economy in Environmental Studies
Acknowledgements
6
Contents
7
1 Introduction
12
2 Classifying Individual Samples into Oneof Two Categories
19
2.1 Introduction
19
2.2 Presence/Absence Measurements
21
2.2.1 Exhaustive Retesting
22
2.2.2 Sequential Retesting
25
2.2.3 Binary Split Retesting
28
2.2.4 Curtailed Exhaustive Retesting
33
2.2.5 Curtailed Sequential Retesting
37
2.2.6 Curtailed Binary Split Retesting
41
2.2.7 Entropy-Based Retesting
43
2.2.8 Exhaustive Retesting in the Presence of Classification Errors
48
2.2.9 Other Costs
50
2.3 Continuous Response Variables
51
2.3.1 Quantitatively Curtailed Exhaustive Retesting
55
2.3.2 Binary Split Retesting
56
2.3.3 Entropy-Based Retesting
59
2.4 Cost Analysis of Composite Sampling for Classification
59
2.4.1 Introduction
59
2.4.2 General Cost Expression
59
2.4.3 Effect of False Positives and False Negatives on Composite Sample Classification
60
2.4.4 Presence/Absence Measurements
61
2.4.5 Continuous Measurements
63
3 Identifying Extremely Large Observations
64
3.1 Introduction
64
3.2 Prediction of the Sample Maximum
65
3.3 The Sweep-Out Method to Identify the Sample Maximum
67
3.4 Extensive Search of Extreme Values
68
3.5 Application
69
3.6 Two-Way Composite Sampling Design
77
3.7 Illustrative Example
79
3.8 Analysis of Composite Sampling Data Using the Principle of Maximum Entropy
85
3.8.1 Introduction
85
3.8.2 Modeling Composite Sampling Using the Principle of Maximum Entropy
86
3.8.3 When Is the Maximum Entropy Model Reasonable in Practice?
87
4 Estimating Prevalence of a Trait
89
4.1 Introduction
89
4.2 The Maximum Likelihood Estimator
90
4.3 Alternative Estimators
92
4.4 Comparison Between p and p
93
4.5 Estimation of Prevalence in Presence of Measurement Error
93
5 A Bayesian Approach to the Classification Problem
95
5.1 Introduction
95
5.2 Bayesian Updating of p
98
5.3 Minimization of the Expected Relative Cost
101
5.4 Discussion
103
6 Inference on Mean and Variance
105
6.1 Introduction
105
6.2 Notation and Basic Results
106
6.2.1 Notation
106
6.2.2 Basic Results
107
6.3 Estimation Without Measurement Error
109
6.4 Estimation in the Presence of Measurement Error
111
6.5 Maintaining Precision While Reducing Cost
112
6.6 Estimation of 2x and 2
113
6.7 Estimation of Population Variance
114
6.8 Confidence Interval for the Population Mean
117
6.9 Tests of Hypotheses in the Population Mean
118
6.9.1 One-Sample Tests
118
6.9.2 Two-Sample Tests
119
6.10 Applications
120
6.10.1 Comparison of Arithmetic Averages of Soil pH Values with the pH Values of Composite Samples
120
6.10.2 Comparison of Random and Composite Sampling Methods for the Estimation of Fat Contents of Bulk Milk Supplies
120
6.10.3 Optimization of Sampling for the Determination of Mean Radium-226 Concentration in Surface Soil
121
7 Composite Sampling with Random Weights
123
7.1 Introduction
123
7.2 Expected Value, Variance, and Covariance of Bilinear Random Forms
124
7.3 Models for the Weights
126
7.3.1 Assumptions on the First Two Moments
127
7.3.2 Distributional Assumptions
127
7.4 The Model for Composite Sample Measurements
129
7.4.1 Subsampling a Composite Sample
129
7.4.2 Several Composite Samples
132
7.4.3 Subsampling of Several Composite Samples
133
7.4.4 Measurement Error
134
7.5 Applications
136
7.5.1 Sampling Frequency and Comparison of Graband Composite Sampling Programs for Effluents
136
7.5.2 Theoretical Comparison of Grab and Composite Sampling Programs
136
7.5.3 Grab vs. Composite Sampling: A Primer for the Manager and Engineer
137
7.5.4 Composite Samples Overestimate Waste Loads
137
7.5.5 Composite Samples for Foliar Analysis
140
7.5.6 Lateral Variability of Forest Floor Properties Under Second-Growth Douglas-Fir Stands and the Usefulness of Composite SamplingTechniques
141
8 A Linear Model for Estimation with Composite Sample Data
143
8.1 Introduction
143
8.2 Motivation for a Unified Model
144
8.3 The Model
145
8.4 Discussion of the Assumptions
147
8.4.1 The Structural/Sampling Submodel
147
8.4.2 The Compositing/Subsampling Submodel
148
8.4.3 The Structure of the Matrices W, MW, and W
148
8.5 Moments of x and y
154
8.6 Complex Sampling Schemes Before Compositing
154
8.6.1 Segmented Populations
155
8.6.2 Estimating the Mean in Segmented Populations
155
8.6.3 Estimating Variance Components in Segmented Populations
158
8.7 Estimating the Effect of a Binary Factor
161
8.7.1 Fully Segregated Composites
165
8.7.2 Fully Confounded Composites
169
8.8 Elementary Matrices and Kronecker Products
172
8.8.1 Decomposition of Block Matrices
173
8.9 Expectation and Dispersion Matrix When Both W and x Are Random
176
8.9.1 The Expectation of Wx
176
8.9.2 Variance/Covariance Matrix of Wx
180
9 Composite Sampling for Site Characterization and Cleanup Evaluation
182
9.1 Data Quality Objectives
182
9.2 Optimal Composite Designs
185
9.2.1 Cost of a Sampling Program
186
9.2.2 Optimal Allocation of Resources
186
9.2.3 Power of a Test and Determination of Sample Size
187
9.2.4 Algorithms for Determination of Sample Size
188
10 Spatial Structures of Site Characteristics and Composite Sampling
190
10.1 Introduction
190
10.2 Models for Spatial Processes
190
10.2.1 Composite Sampling
194
10.3 Application to Two Superfund Sites
197
10.3.1 The Two Sites
197
10.3.2 Methods
198
10.3.3 Results
199
10.3.4 Discussion
202
10.4 Compositing by Spatial Contiguity
205
10.4.1 Introduction
205
10.4.2 Retesting Strategies
206
10.4.3 Composite Sample-Forming Schemes
207
10.5 Compositing of Ranked Set Samples
208
10.5.1 Ranked Set Sampling
208
10.5.2 Relative Precision of the RSS Estimatorof a Population Mean Relative to Its SRS Estimator
211
10.5.3 Unequal Allocation of Sample Sizes
212
10.5.4 Formation of Homogeneous Composite Samples
213
11 Composite Sampling of Soils and Sediments
215
11.1 Detection of Contamination
215
11.1.1 Detecting PCB Spills
215
11.1.2 Compositing Strategy for Analysis of Samples
217
11.2 Estimation of the Average Level of Contamination
219
11.2.1 Estimation of the Average PCB Concentrationon the Spill Area
219
11.2.2 Onsite Surface Soil Sampling for PCBat the Armagh Site
220
11.2.3 The Armagh Site
221
11.2.4 Simulating Composite Samples
224
11.2.5 Locating Individual Samples with High PCB Concentrations
227
11.3 Estimation of Trace Metal Storage in Lake St. Clair Post-settlement Sediments Using Composite Samples
228
12 Composite Sampling of Liquids and Fluids
232
12.1 Comparison of Random and Composite Sampling Methodsfor the Estimation of Fat Content of Bulk Milk Supplies
232
12.1.1 Experiment
232
12.1.2 Estimation Methods
233
12.1.3 Results
233
12.1.4 Composite Compared with Yield-Weighted Estimate of Fat Percentage
234
12.2 Composite Sampling of Highway Runoff
234
12.3 Composite Samples Overestimate Waste Loads
237
13 Composite Sampling and Indoor Air Pollution
240
13.1 Household Dust Samples
240
14 Composite Sampling and Bioaccumulation
243
14.1 Example: National Human Adipose Tissue Survey
245
14.2 Results from the Analysis of 1987 NHATS Data
245
Glossary and Terminology
247
Bibliography
253
Index
271
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