Spatio-temporal Design

Contributors xv

Foreword xix

1 Collecting spatio-temporal data 1
Jorge Mateu and Werner G. Müller

1.1 Introduction 1

1.2 Paradigms in spatio-temporal design 2

1.3 Paradigms in spatio-temporal modeling 3

1.4 Geostatistics and spatio-temporal random functions 4

1.4.1 Relevant spatio-temporal concepts 4

1.4.2 Properties of the spatio-temporal covariance and variogram functions 6

1.4.3 Spatio-temporal kriging 8

1.4.4 Spatio-temporal covariance models 10

1.4.5 Parametric estimation of spatio-temporal covariograms 11

1.5 Types of design criteria and numerical optimization 13

1.6 The problem set: Upper Austria 17

1.6.1 Climatic data 17

1.6.2 Grassland usage 18

1.7 The chapters 23

Acknowledgments 28

References 28

2 Model-based frequentist design for univariate and multivariate geostatistics 37
Dale L. Zimmerman and Jie li

2.1 Introduction 37

2.2 Design for univariate geostatistics 38

2.2.1 Data-model framework 38

2.2.2 Design criteria 38

2.2.3 Algorithms 42

2.2.4 Toy example 42

2.3 Design for multivariate geostatistics 45

2.3.1 Data-model framework 45

2.3.2 Design criteria 47

2.3.3 Toy example 48

2.4 Application: Austrian precipitation data network 50

2.5 Conclusions 52

References 53

3 Model-based criteria heuristics for second-phase spatial sampling 54
Eric M. Delmelle

3.1 Introduction 54

3.2 Geometric and geostatistical designs 56

3.2.1 Efficiency of spatial sampling designs 56

3.2.2 Sampling spatial variables in a geostatistical context 57

3.2.3 Sampling designs minimizing the kriging variance 58

3.3 Augmented designs: Second-phase sampling 59

3.3.1 Additional sampling schemes to maximize change in the kriging variance 59

3.3.2 A weighted kriging variance approach 60

3.4 A simulated annealing approach 63

3.5 Illustration 65

3.5.1 Initial sampling designs 66

3.5.2 Augmented designs 68

3.6 Discussion 68

References 69

4 Spatial sampling design by means of spectral approximations to the error process 72
Gunter Spöck and Jürgen Pilz

4.1 Introduction 72

4.2 A brief review on spatial sampling design 75

4.3 The spatial mixed linear model 76

4.4 Classical Bayesian experimental design problem 77

4.5 The Smith and Zhu design criterion 79

4.6 Spatial sampling design for trans-Gaussian kriging 81

4.7 The spatDesign toolbox 82

4.7.1 Covariance estimation and variography software 83

4.7.2 Spatial interpolation and kriging software 84

4.7.3 Spatial sampling design software 85

4.8 An example session 89

4.8.1 Preparatory calculations 89

4.8.2 Optimal design for the BSLM 93

4.8.3 Design for the trans-Gaussian kriging 94

4.9 Conclusions 98

References 99

5 Entropy-based network design using hierarchical Bayesian kriging 103
Baisuo Jin, Yuehua Wu and Baiqi Miao

5.1 Introduction 103

5.2 Entropy-based network design using hierarchical Bayesian kriging 105

5.3 The data 107

5.4 Spatio-temporal modeling 107

5.5 Obtaining a staircase data structure 111

5.6 Estimating the hyperparameters H g and the spatial correlations between gauge stations 113

5.7 Spatial predictive distribution over the 445 areas located in the 18 districts of Upper Austria 117

5.8 Adding gauge stations over the 445 areas located in the 18 districts of Upper Austria 120

5.9 Closing down an existing gauge station 122

5.10 Model evaluation 124

Appendix 5.1: Hierarchical Bayesian spatio-temporal modeling (or kriging) 124

Appendix 5.2: Some estimated parameters 128

Acknowledgments 129

References 129

6 Accounting for design in the analysis of spatial data 131
Brian J. Reich and Montserrat Fuentes

6.1 Introduction 131

6.2 Modeling approaches 134

6.2.1 Informative missingness 134

6.2.2 Informative sampling 135

6.2.3 A two-stage approach for informative sampling 136

6.3 Analysis of the Austrian precipitation data 137

6.4 Discussion 139

References 141

7 Spatial design for knot selection in knot-based dimension reduction models 142
Alan E. Gelfand, Sudipto Banerjee and Andrew O. Finley

7.1 Introduction 142

7.2 Handling large spatial datasets 145

7.3 Dimension reduction approaches 146

7.3.1 Basic properties of low rank models 146

7.3.2 Predictive process models: A brief review 148

7.4 Some basic knot design ideas 149

7.4.1 A brief review of spatial design 149

7.4.2 A strategy for selecting knots 151

7.5 Illustrations 153

7.5.1 A simulation example 153

7.5.2 A simulation example using the two-step analysis 159

7.5.3 Tree height and diameter analysis 160

7.5.4 Austria precipitation analysis 162

7.6 Discussion and future work 165

References 166

8 Exploratory designs for assessing spatial dependence 170
Agnes Fussl, Werner G. Müller and Juan Rodríguez-Díaz

8.1 Introduction 170

8.1.1 The dataset and its visualization 172

8.2 Spatial links 174

8.2.1 Spatial neighbors 175

8.2.2 Spatial weights 176

8.3 Measures of spatial dependence 178

8.4 Models for areal data 180

8.4.1 H₀ : A spaceless regression model 181

8.4.2 H₀ : Spatial regression models 185

8.5 Design considerations 190

8.5.1 A design criterion 192

8.5.2 Example 194

8.6 Discussion 195

Appendix 8.1: R code 198

Acknowledgments 202

References 203

9 Sampling design optimization for space-time kriging 207
Gerard B.M. Heuvelink, Daniel A. Griffith, Tomislav Hengl and Stephanie J. Melles

9.1 Introduction 207

9.2 Methodology 209

9.2.1 Space-time universal kriging 209

9.2.2 Sampling design optimization with spatial simulated annealing 211

9.3 Upper Austria case study 212

9.3.1 Descriptive statistics 212

9.3.2 Estimation of the space-time model and universal kriging 215

9.3.3 Optimal design scenario 1 218

9.3.4 Optimal design scenario 2 219

9.3.5 Optimal design scenario 3 219

9.4 Discussion and conclusions 221

Appendix 9.1: R code 222

Acknowledgment 227

References 228

10 Space-time adaptive sampling and data transformations 231
José M. Angulo, María C. Bueso and Francisco J. Alonso

10.1 Introduction 231

10.2 Adaptive sampling network design 233

10.2.1 A simulated illustration 235

10.3 Predictive information based on data transformations 238

10.4 Application to Upper Austria temperature data 242

10.5 Summary 246

Acknowledgments 247

References 247

11 Adaptive sampling design for spatio-temporal prediction 249
Thomas R. Fanshawe and Peter J. Diggle

11.1 Introduction 249

11.2 Review of spatial and spatio-temporal adaptive designs 251

11.3 The stationary Gaussian model 253

11.3.1 Model specification 253

11.3.2 Theoretically optimal designs 254

11.3.3 A comparison of design strategies 254

11.4 The dynamic process convolution model 257

11.4.1 Model specification 257

11.4.2 A comparison of design strategies 258

11.5 Upper Austria rainfall data example 262

11.6 Discussion 264

Appendix 11.1 266

References 267

12 Semiparametric dynamic design of monitoring networks for non-Gaussian spatio-temporal data 269
Scott H. Holan and Christopher K. Wikle

12.1 Introduction 269

12.2 Semiparametric non-Gaussian space-time dynamic design 271

12.2.1 Semiparametric spatio-temporal dynamic Gamma model 271

12.2.2 Simulation-based dynamic design 274

12.2.3 Extended Kalman filter for dynamic gamma models 275

12.2.4 Extended Kalman filter design algorithm 277

12.3 Application: Upper Austria precipitation 278

12.4 Discussion 282

Acknowledgments 282

References 283

13 Active learning for monitoring network optimization 285
Devis Tuia, Alexei Pozdnoukhov, Loris Foresti and Mikhail Kanevski

13.1 Introduction 285

13.2 Statistical learning from data 287

13.2.1 Algorithmic approaches to learning 288

13.2.2 Over-fitting and model selection 288

13.3 Support vector machines and kernel methods 289

13.3.1 Classification: SVMs 290

13.3.2 Density estimation: One-class SVM 292

13.3.3 Regression: Kernel ridge regression 293

13.3.4 Regression: SVR 294

13.4 Active learning 294

13.4.1 A general framework 295

13.4.2 First steps in active learning: Reducing output variance 296

13.4.3 Exploration-exploitation strategies: Towards mixed approaches 297

13.5 Active learning with SVMs 297

13.5.1 Margin sampling 297

13.5.2 Diversity of batches of samples 299

13.5.3 Committees of models 299

13.6 Case studies 300

13.6.1 Austrian climatological data 300

13.6.2 Cesium-137 concentration after Chernobyl 304

13.6.3 Wind power plants sites evaluation 307

13.7 Conclusions 312

Acknowledgments 314

References 314

14 Stationary sampling designs based on plume simulations 319
Kristina B. Helle and Edzer Pebesma

14.1 Introduction 319

14.2 Plumes: From random fields to simulations 320

14.3 Cost functions 324

14.3.1 Detecting plumes 324

14.3.2 Mapping and characterising plumes 325

14.3.3 Combined cost functions 325

14.4 Optimisation 326

14.4.1 Greedy search 326

14.4.2 Spatial simulated annealing 328

14.4.3 Genetic algorithms 329

14.4.4 Other methods 331

14.4.5 Evaluation and sensitivity 331

14.4.6 Use case: Combination and comparison of optimisation algorithms 332

14.5 Results 334

14.5.1 Simulations 334

14.5.2 Greedy search 335

14.5.3 Sensitivity of greedy search to the plume simulations 336

14.5.4 Comparison of optimisation algorithms 337

14.6 Discussion 340

Acknowledgments 341

References 341

Index 345