Spatio-temporal Design

Contributors xv Foreword xix 1 Collecting spatio-temporal data 1 Jorge Mateu and Werner G. Muller 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 Spock and Jurgen 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 Hg 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. Muller and Juan Rodr?guez-D?az 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 Jos´e M. Angulo, Mar´?a 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