Spatio-Temporal Design: Advances in Efficient Data Acquisition

Foreword 1 Collecting Spatio-temporal Data 1.1 Introduction 1.2 Paradigms in Spatio-temporal Design 1.3 Paradigms in Spatio-temporal Modeling 1.4 Geostatistics and spatio-temporal random functions 1.4.1 Relevant spatio-temporal concepts 1.4.2 Properties of the spatio-temporal covariance and variogram functions 1.4.3 Spatio-temporal kriging 1.4.4 Spatio-temporal covariance models 1.4.5 Parametric estimation of spatio-temporal covariograms 1.5 Types of Design Criteria and Numerical Optimization 1.6 The Problem Set: Upper Austria 1.6.1 Climatic data 1.6.2 Grassland usage 1.7 The Chapters 1.8 Acknowledgments References 2 Model-Based Frequentist Design for Univariate and Multivariate Geostatistics 2.1 Introduction 2.2 Design for Univariate Geostatistics 2.2.1 Data-model framework 2.2.2 Design criteria 2.2.3 Algorithms 2.2.4 Toy example 2.3 Design for Multivariate Geostatistics 2.3.1 Data-model framework 2.3.2 Design criteria 2.3.3 Toy example 2.4 Application: Austrian Precipitation Data Network 2.5 Conclusions References 3 Model-based criteria and for second-phase spatial sampling 3.1 Introduction 3.2 Geometric and geostatistical designs 3.3 Augmented designs: second-phase sampling 3.3.1 Additional Sampling Schemes to Minimize the kriging Variance 3.3.2 A weighted kriging variance approach 3.4 A simulated annealing approach 3.5 Illustration: 3.6 Discussion: References/Further Reading and Bibliography 4 Spatial sampling design by means of spectral approximations to the error process 4.1 Introduction 4.2 A brief review on spatial sampling design 4.3 The spatial mixed linear model 4.4 Classical Bayesian experimental design problem 4.5 The Smith and Zhu design criterion 4.6 Spatial sampling design for trans-Gaussian kriging 4.7 The spatDesign toolbox 4.7.1 Covariance estimation and variography software 4.7.2 Spatial interpolation and kriging software 4.7.3 Spatial sampling design software 4.8 An example session 4.8.1 Preparatory calculations 4.8.2 Optimal design for the BSLM 4.8.3 Design for the trans-Gaussian kriging 4.9 Conclusions References/Further Reading and Bibliography 5 Entropy-based network design using hierarchical Bayesian kriging 5.1 Introduction 1 5.2 Entropy-based network design using hierarchical Bayesian kriging 5.3 The data 5.4 Spatio-temporal modeling 5.5 Obtain a staircase data structure 5.6 Estimate the hyperparameters Hg and the spatial correlations between gauge stations 5.7 Spatial predictive distribution over the 445 areas located in the 18 districts of Upper-Austria. 5.8 Add gauge stations among the 445 areas located in the 18 districts of Upper-Austria 5.9 Close down an existing gauge station 5.10 Model evaluation References/Further Reading and Bibliography 6 Accounting for design in the analysis of spatial data 6.1 Introduction 6.2 Modeling approaches 6.2.1 Informative missingness 6.2.2 Informative sampling 6.2.3 A two-stage approach for informative sampling 6.3 Analysis of the Austrian precipitation data 6.4 Discussion References/Further Reading and Bibliography 7 Spatial design for knot selection in knot-based dimension reduction models 7.1 Introduction 7.2 Handling large spatial datasets 7.3 Dimension reduction approaches 7.3.1 Basic properties of low rank models 7.3.2 Predictive process models: A brief review 7.4 Some basic knot design ideas 7.4.1 A brief review of spatial design 7.4.2 A strategy for selecting knots 7.5 Illustrations 7.5.1 A simulation example 7.5.2 A simulation example using the two step analysis 7.5.3 Tree height and diameter analysis 7.5.4 Austria precipitation analysis 7.6 Discussion and future work 8 Exploratory Designs for Assessing Spatial Dependence 8.1 Introduction 8.2 The data set and its visualization 8.3 Spatial links 8.3.1 Spatial neighbors 8.3.2 Spatial weights 8.4 Measures of Spatial Dependence 8.5 Models for areal data 8.5.1 H0: a spaceless regression model 8.5.2 HA: spatial regression models 8.6 Design considerations 8.6.1 A Design Criterion 8.6.2 Example 8.7 Discussion 8.8 Appendix: R Code 8.9 Acknowledgement References References/Further Reading and Bibliography 9 Sampling design optimization for space-time kriging 9.1 Introduction 9.2 Methodology 9.2.1 Space-time universal kriging 9.2.2 Sampling design optimization with spatial simulated annealing 9.3 Upper-Austria case study 9.3.1 Descriptive statistics 9.3.2 Estimation of the space-time model and universal kriging 9.3.3 Optimal design scenario 1 9.3.4 Optimal design scenario 2 9.3.5 Optimal design scenario 3 9.4 Discussion and Conclusions 9.5 Appendix: R Code 9.6 Acknowledgements References/Further Reading and Bibliography 10 Space-Time Adaptive Sampling and Data Transformations 10.1 Introduction 10.2 Adaptive Sampling Network Design 10.2.1 A simulated illustration 10.3 Predictive Information based on Data Transformations 10.4 Application to Upper Austria Temperature Data 10.5 Summary References/Further Reading and Bibliography 11 Adaptive Sampling Design for Spatio-Temporal Prediction 11.1 Introduction 11.2 Review of Spatial and Spatio-Temporal Adaptive Designs 11.3 The Stationary Gaussian Model 11.3.1 Model specification 11.3.2 Theoretically optimal designs 11.3.3 A comparison of design strategies 11.4 The Dynamic Process Convolution Model 11.4.1 Model specification 11.4.2 A comparison of design strategies 11.5 Upper Austria Rainfall Data Example 11.6 Discussion References/Further Reading and Bibliography 12 Semiparametric Dynamic Design of Monitoring Networks for Non-Gaussian Spatio-temporal Data 12.1 Introduction 12.2 Semiparametric Non-Gaussian Space-Time Dynamic Design 12.2.1 Semiparametric Spatio-temporal Dynamic Gamma Model 12.2.2 Simulation-Based Dynamic Design 12.2.3 Extended Kalman Filter for Dynamic Gamma Models 12.2.4 Extended Kalman Filter Design Algorithm 12.3 Application: Upper Austria Precipitation 12.4 Discussion References/Further Reading and Bibliography 13 Active learning for monitoring network optimization 13.1 Introduction 13.2 Statistical Learning from Data 13.2.1 Algorithmic approaches to learning 13.2.2 Over-fitting and model selection 13.3 Support Vector Machines and Kernel Methods 13.3.1 Classification: Support vector machines 13.3.2 Density estimation: one class SVM 13.3.3 Regression: kernel ridge regression 13.3.4 Regression: support vector regression 13.4 Active Learning 13.4.1 A general framework 13.4.2 First steps in active learning: reducing output variance 13.4.3 Exploration-exploitation strategies: towards mixed approaches 13.5 Active Learning with SVMs 13.5.1 Margin sampling 13.5.2 Diversity of batches of samples 13.5.3 Committees of models 13.6 Case studies 13.6.1 Austrian climatological data 13.6.2 Cesium-137 concentration after Chernobyl 13.6.3 Wind power plants sites evaluation 13.7 Conclusions References/Further Reading and Bibliography 14 Stationary Sampling Designs Based on Plume Simulations 14.1 Plumes: From Random Fields to Simulations 14.2 Cost Functions 14.2.1 Detecting plumes 14.2.2 Mapping and characterising plumes 14.2.3 Combined cost functions 14.3 Optimisation 14.3.1 Greedy search 14.3.2 Spatial simulated annealing 14.3.3 Genetic algorithms 14.3.4 Other methods 14.3.5 Evaluation and sensitivity 14.3.6 Use case: combination and comparison of optimisation algorithms 14.4 Results 14.4.1 Simulations 14.4.2 Greedy search 14.4.3 Sensitivity of greedy search to the plume simulations 14.4.4 Comparison of optimisation algorithms 14.5 Discussion References/Further Reading and Bibliography Index