Modern Spatiotemporal Geostatistics

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ISBN: 9780486488189 | 0486488187
Cover: Paperback
Copyright: 7/17/2012

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This introductory scholarly treatment explores the fundamentals of modern geostatistics, a group of spatiotemporal concepts and methods related to the advancement of the epistemic status of stochastic data analysis. Christakos considers the role of geostatistics in improved mathematical models of scientific mapping, and focuses on the Bayesian maximum entropy approach for studying spatiotemporal distributions of natural variables. 2000 edition.

Preface	p. vii
Spatiotemporal Mapping in Natural Sciences	p. 1
Mapping Fundamentals	p. 1
The Epistemic Status of Modern Spatiotemporal Geostatistics: It Pays to Theorize!	p. 11
Why Modern Geostatistics?	p. 14
Scientific content	p. 15
Indetermination thesis	p. 16
Spatiotemporal geometry	p. 19
Sources of physical knowledge	p. 20
The non-Procrustean spirit	p. 20
Bayesian Maximum Entropy Space/Time Analysis and Mapping	p. 21
BME features	p. 22
The Integration Capability of Modern Spatiotemporal Geostatistics	p. 23
The "Knowledge-Map" Approach	p. 24
Spatiotemporal Geometry	p. 25
A More Realistic Concept	p. 25
The Spatiotemporal Continuum Idea	p. 26
The Coordinate System	p. 32
Euclidean coordinate systems	p. 35
Non-Euclidean coordinate systems	p. 38
Metrical Structure	p. 42
Separate metrical structures	p. 43
Composite metrical structures	p. 50
Some comments on physical spatiotemporal geometry	p. 52
The Field Idea	p. 54
Restrictions on spatiotemporal geometry imposed by field measurements and natural media	p. 54
Restrictions on spatiotemporal geometry imposed by physical laws	p. 56
The Complementarity Idea	p. 58
Putting Things Together: The Spatiotemporal Random Field Concept	p. 59
Correlation analysis and spatiotemporal geometry	p. 61
Permissibility criteria and spatiotemporal geometry	p. 64
Effect of spatiotemporal geometry on mapping	p. 66
Some Final Thoughts	p. 69
Physical Knowledge	p. 71
From the General to the Specific	p. 71
The General Knowledge Base	p. 73
A mathematical formulation of the general knowledge base	p. 74
General knowledge in terms of statistical moments	p. 75
General knowledge in terms of physical laws	p. 76
Some other forms of general knowledge	p. 81
The Specificatory Knowledge Base	p. 82
Specificatory knowledge in terms of hard data	p. 84
Specificatory knowledge in terms of soft data	p. 85
Summa Theologica	p. 87
The Epistemic Paradigm	p. 89
Acquisition and Processing of Physical Knowledge	p. 89
Epistemic Geostatistics and the BME Analysis	p. 90
Prior stage	p. 92
Meta-prior stage	p. 94
Integration or posterior stage	p. 95
Conditional Probability of a Spatiotemporal Map and its Relation to the Probability of Conditionals	p. 98
Material and strict map conditionals	p. 98
Other map conditionals	p. 100
The BME Net	p. 101
Mathematical Formulation of the BME Method	p. 103
A Pragmatic Framework of the Mapping Problem	p. 103
The Prior Stage	p. 104
Map information measures in light of general knowledge	p. 104
General knowledge-based map pdf	p. 106
General knowledge in the form of random field statistics (including multiple-point statistics)	p. 107
General knowledge in the form of physical laws	p. 109
Possible modifications and generalizations of the prior stage	p. 118
The Meta-Prior Stage	p. 119
The Integration or Posterior Stage	p. 120
The Structure of the Modern Spatiotemporal Geostatistics Paradigm	p. 122
The Two Legs on Which the BME Equations Stand	p. 123
Analytical Expressions of the Posterior Operator	p. 125
Specificatory Knowledge and Single-Point Mapping	p. 125
Posterior Operators for Interval and Probabilistic Soft Data	p. 126
Posterior Operators for Other Forms of Soft Data	p. 130
Discussion	p. 132
The Choice of a Spatiotemporal Estimate	p. 135
Versatility of the BME Approach	p. 135
The BMEmode Estimate	p. 136
Statistics-Hard and soft data	p. 138
Physical laws-Hard and soft data	p. 142
The West Lyons Porosity Field	p. 143
Other BME Estimates	p. 147
A Matter of Coordination	p. 148
Uncertainty Assessment	p. 149
Mapping Accuracy	p. 149
Symmetric Posteriors	p. 150
Asymmetric Posteriors	p. 153
The Equus Beds Aquifer	p. 155
The study area	p. 155
Data collection	p. 156
The water-level elevation model	p. 158
BME water-level elevation mapping	p. 158
Optimal decision making	p. 163
Doing Progressive Guesswork	p. 164
Modifications of Formal BME Analysis	p. 165
Versatility and Practicality	p. 165
Functional BME Analysis	p. 166
General formulation	p. 166
The support effect	p. 168
Multivariable or Vector BME Analysis	p. 170
General formulation	p. 170
Physical laws	p. 172
Transformation laws	p. 173
Decision making	p. 174
Multipoint BME Analysis	p. 175
Multipoint BME estimation	p. 175
Multipoint BME uncertainty assessment	p. 177
BME in the Context of Systems Analysis	p. 181
Risk analysis of natural systems	p. 181
Human-exposure systems	p. 182
Associations between environmental exposure arid health effect	p. 183
Bringing Plato and Odysseus Together	p. 195
Single-Point Analytical Formulations	p. 197
The Basic Single-Point BME Equations	p. 197
Ordinary Covariance and Variogram-Hard and Soft Data	p. 198
Particulate Matter Distributions in North Carolina	p. 203
Generalized Covariance-Hard and Soft Data	p. 211
Some Non-Gaussian Analytical Expressions	p. 213
Theory, Practice, and Computers	p. 216
Multipoint Analytical Formulations	p. 217
The Basic Multipoint BME Equations	p. 217
Ordinary Covariance-Hard and Soft Data	p. 218
Ordinary Variogram-Hard and Soft Data	p. 222
Other Combinations	p. 223
Spatiotemporal Covariance and Variogram Models	p. 224
Separable models	p. 224
Nonseparable models	p. 225
And Still the Garden Grows!	p. 228
Popular Methods in the Light of Modern Spatiotemporal Geostatistics	p. 229
The Generalization Power of BME	p. 229
Minimum Mean Squared Error Estimators	p. 230
Kriging Estimators	p. 233
Simple and ordinary kriging	p. 233
Lognormal kriging	p. 244
Nonhomogeneous/nonstationary kriging	p. 244
Indicator kriging	p. 246
Other sorts of kriging	p. 249
Limitations of kriging techniques-Advantages of BME analysis	p. 249
Random Field Models of Modern Spatiotemporal Geostatistics	p. 251
A unified framework	p. 251
The class of coarse-grained RF	p. 254
The class of S/TRF-¿¿ models in heterogeneity analysis	p. 254
The class of space/time fractal RF models	p. 256
The class of wavelet RF	p. 257
The Emergence of the Computational Viewpoint in BME Analysis	p. 260
Modern Spatiotemporal Geostatistics and GIS Integration Technologies	p. 261
A Call Not to Arms but to Research	p. 265
Unification and Distinction	p. 265
The Formal Part	p. 266
Interpretive BME and the Search for "Rosebud"	p. 267
The Argument of Modern Spatiotemporal Geostatistics	p. 268
The Ending as a New Beginning	p. 271
Bibliography	p. 273
Index	p. 283
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Modern Spatiotemporal Geostatistics

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