Info
- Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.
Modeling uncertainty in the earth sciences / / Jef Caers
| Modeling uncertainty in the earth sciences / / Jef Caers |
| Autore | Caers Jef |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, 2011 |
| Descrizione fisica | 1 online resource (240 p.) |
| Disciplina | 551.01/5195 |
| Soggetto topico |
Geology - Mathematical models
Earth sciences - Statistical methods Three-dimensional imaging in geology Uncertainty |
| ISBN |
1-283-17797-8
1-119-99871-9 1-119-99593-0 1-119-99592-2 9786613177971 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Modeling Uncertainty in the Earth Sciences -- Contents -- Preface -- Acknowledgements -- 1 Introduction -- 1.1 Example Application -- 1.1.1 Description -- 1.1.2 3D Modeling -- 1.2 Modeling Uncertainty -- Further Reading -- 2 Review on Statistical Analysis and Probability Theory -- 2.1 Introduction -- 2.2 Displaying Data with Graphs -- 2.2.1 Histograms -- 2.3 Describing Data with Numbers -- 2.3.1 Measuring the Center -- 2.3.2 Measuring the Spread -- 2.3.3 Standard Deviation and Variance -- 2.3.4 Properties of the Standard Deviation -- 2.3.5 Quantiles and the QQ Plot -- 2.4 Probability -- 2.4.1 Introduction -- 2.4.2 Sample Space, Event, Outcomes -- 2.4.3 Conditional Probability -- 2.4.4 Bayes' Rule -- 2.5 Random Variables -- 2.5.1 Discrete Random Variables -- 2.5.2 Continuous Random Variables -- 2.5.2.1 Probability Density Function (pdf) -- 2.5.2.2 Cumulative Distribution Function -- 2.5.3 Expectation and Variance -- 2.5.3.1 Expectation -- 2.5.3.2 Population Variance -- 2.5.4 Examples of Distribution Functions -- 2.5.4.1 The Gaussian (Normal) Random Variable and Distribution -- 2.5.4.2 Bernoulli Random Variable -- 2.5.4.3 Uniform Random Variable -- 2.5.4.4 A Poisson Random Variable -- 2.5.4.5 The Lognormal Distribution -- 2.5.5 The Empirical Distribution Function versus the Distribution Model -- 2.5.6 Constructing a Distribution Function from Data -- 2.5.7 Monte Carlo Simulation -- 2.5.8 Data Transformations -- 2.6 Bivariate Data Analysis -- 2.6.1 Introduction -- 2.6.2 Graphical Methods: Scatter plots -- 2.6.3 Data Summary: Correlation (Coefficient) -- 2.6.3.1 Definition -- 2.6.3.2 Properties of r -- Further Reading -- 3 Modeling Uncertainty: Concepts and Philosophies -- 3.1 What is Uncertainty? -- 3.2 Sources of Uncertainty -- 3.3 Deterministic Modeling -- 3.4 Models of Uncertainty -- 3.5 Model and Data Relationship.
3.6 Bayesian View on Uncertainty -- 3.7 Model Verification and Falsification -- 3.8 Model Complexity -- 3.9 Talking about Uncertainty -- 3.10 Examples -- 3.10.1 Climate Modeling -- 3.10.1.1 Description -- 3.10.1.2 Creating Data Sets Using Models -- 3.10.1.3 Parameterization of Subgrid Variability -- 3.10.1.4 Model Complexity -- 3.10.2 Reservoir Modeling -- 3.10.2.1 Description -- 3.10.2.2 Creating Data Sets Using Models -- 3.10.2.3 Parameterization of Subgrid Variability -- 3.10.2.4 Model Complexity -- Further Reading -- 4 Engineering the Earth: Making Decisions Under Uncertainty -- 4.1 Introduction -- 4.2 Making Decisions -- 4.2.1 Example Problem -- 4.2.2 The Language of Decision Making -- 4.2.3 Structuring the Decision -- 4.2.4 Modeling the Decision -- 4.2.4.1 Payoffs and Value Functions -- 4.2.4.2 Weighting -- 4.2.4.3 Trade-Offs -- 4.2.4.4 Sensitivity Analysis -- 4.3 Tools for Structuring Decision Problems -- 4.3.1 Decision Trees -- 4.3.2 Building Decision Trees -- 4.3.3 Solving Decision Trees -- 4.3.4 Sensitivity Analysis -- Further Reading -- 5 Modeling Spatial Continuity -- 5.1 Introduction -- 5.2 The Variogram -- 5.2.1 Autocorrelation in 1D -- 5.2.2 Autocorrelation in 2D and 3D -- 5.2.3 The Variogram and Covariance Function -- 5.2.4 Variogram Analysis -- 5.2.4.1 Anisotropy -- 5.2.4.2 What is the Practical Meaning of a Variogram? -- 5.2.5 A Word on Variogram Modeling -- 5.3 The Boolean or Object Model -- 5.3.1 Motivation -- 5.3.2 Object Models -- 5.4 3D Training Image Models -- Further Reading -- 6 Modeling Spatial Uncertainty -- 6.1 Introduction -- 6.2 Object-Based Simulation -- 6.3 Training Image Methods -- 6.3.1 Principle of Sequential Simulation -- 6.3.2 Sequential Simulation Based on Training Images -- 6.3.3 Example of a 3D Earth Model -- 6.4 Variogram-Based Methods -- 6.4.1 Introduction -- 6.4.2 Linear Estimation. 6.4.3 Inverse Square Distance -- 6.4.4 Ordinary Kriging -- 6.4.5 The Kriging Variance -- 6.4.6 Sequential Gaussian Simulation -- 6.4.6.1 Kriging to Create a Model of Uncertainty -- 6.4.6.2 Using Kriging to Perform (Sequential) Gaussian Simulation -- Further Reading -- 7 Constraining Spatial Models of Uncertainty with Data -- 7.1 Data Integration -- 7.2 Probability-Based Approaches -- 7.2.1 Introduction -- 7.2.2 Calibration of Information Content -- 7.2.3 Integrating Information Content -- 7.2.4 Application to Modeling Spatial Uncertainty -- 7.3 Variogram-Based Approaches -- 7.4 Inverse Modeling Approaches -- 7.4.1 Introduction -- 7.4.2 The Role of Bayes' Rule in Inverse Model Solutions -- 7.4.3 Sampling Methods -- 7.4.3.1 Rejection Sampling -- 7.4.3.2 Metropolis Sampler -- 7.4.4 Optimization Methods -- Further Reading -- 8 Modeling Structural Uncertainty -- 8.1 Introduction -- 8.2 Data for Structural Modeling in the Subsurface -- 8.3 Modeling a Geological Surface -- 8.4 Constructing a Structural Model -- 8.4.1 Geological Constraints and Consistency -- 8.4.2 Building the Structural Model -- 8.5 Gridding the Structural Model -- 8.5.1 Stratigraphic Grids -- 8.5.2 Grid Resolution -- 8.6 Modeling Surfaces through Thicknesses -- 8.7 Modeling Structural Uncertainty -- 8.7.1 Sources of Uncertainty -- 8.7.2 Models of Structural Uncertainty -- Further Reading -- 9 Visualizing Uncertainty -- 9.1 Introduction -- 9.2 The Concept of Distance -- 9.3 Visualizing Uncertainty -- 9.3.1 Distances, Metric Space and Multidimensional Scaling -- 9.3.2 Determining the Dimension of Projection -- 9.3.3 Kernels and Feature Space -- 9.3.4 Visualizing the Data-Model Relationship -- Further Reading -- 10 Modeling Response Uncertainty -- 10.1 Introduction -- 10.2 Surrogate Models and Ranking -- 10.3 Experimental Design and Response Surface Analysis -- 10.3.1 Introduction. 10.3.2 The Design of Experiments -- 10.3.3 Response Surface Designs -- 10.3.4 Simple Illustrative Example -- 10.3.5 Limitations -- 10.4 Distance Methods for Modeling Response Uncertainty -- 10.4.1 Introduction -- 10.4.2 Earth Model Selection by Clustering -- 10.4.2.1 Introduction -- 10.4.2.2 k-Means Clustering -- 10.4.2.3 Clustering of Earth Models for Response Uncertainty Evaluation -- 10.4.3 Oil Reservoir Case Study -- 10.4.4 Sensitivity Analysis -- 10.4.5 Limitations -- Further Reading -- 11 Value of Information -- 11.1 Introduction -- 11.2 The Value of Information Problem -- 11.2.1 Introduction -- 11.2.2 Reliability versus Information Content -- 11.2.3 Summary of the VOI Methodology -- 11.2.3.1 Steps 1 and 2: VOI Decision Tree -- 11.2.3.2 Steps 3 and 4: Value of Perfect Information -- 11.2.3.3 Step 5: Value of Imperfect Information -- 11.2.4 Value of Information for Earth Modeling Problems -- 11.2.5 Earth Models -- 11.2.6 Value of Information Calculation -- 11.2.7 Example Case Study -- 11.2.7.1 Introduction -- 11.2.7.2 Earth Modeling -- 11.2.7.3 Decision Problem -- 11.2.7.4 The Possible Data Sources -- 11.2.7.5 Data Interpretation -- Further Reading -- 12 Example Case Study -- 12.1 Introduction -- 12.1.1 General Description -- 12.1.2 Contaminant Transport -- 12.1.3 Costs Involved -- 12.2 Solution -- 12.2.1 Solving the Decision Problem -- 12.2.2 Buying More Data -- 12.2.2.1 Buying Geological Information -- 12.2.2.2 Buying Geophysical Information -- 12.3 Sensitivity Analysis -- Index. |
| Record Nr. | UNINA-9910877142303321 |
Caers Jef
|
||
| Hoboken, N.J., : Wiley, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Multiple-point geostatistics : stochastic modeling with training images / / Gregoire Mariethoz and Jef Caers
| Multiple-point geostatistics : stochastic modeling with training images / / Gregoire Mariethoz and Jef Caers |
| Autore | Mariethoz Gregoire |
| Pubbl/distr/stampa | Chichester, England ; ; Oxford, England ; ; Hoboken, New Jersey : , : Wiley Blackwell, , 2015 |
| Descrizione fisica | 1 online resource (379 p.) |
| Disciplina | 551.01/5195 |
| Soggetto topico |
Geology - Statistical methods
Geological modeling |
| ISBN |
1-118-66293-8
1-118-66295-4 1-118-66294-6 |
| Classificazione | SCI031000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Multiple-point geostatistics; Contents; Preface; Acknowledgments; Part I Concepts; 1 Hiking in the Sierra Nevada; 1.1 An imaginary outdoor adventure company: Buena Sierra; 1.2 What lies ahead; 2 Spatial estimation based on random function theory; 2.1 Assumptions of stationarity; 2.2 Assumption of stationarity in spatial problems; 2.3 The kriging solution; 2.3.1 Unbiasedness condition; 2.3.2 Minimizing squared loss; 2.4 Estimating covariances; 2.5 Semivariogram modeling; 2.6 Using a limited neighborhood; 2.7 Universal kriging; 2.8 Semivariogram modeling for universal kriging
2.9 Simple trend example case2.10 Nonstationary covariances; 2.11 Assessment; References; 3 Universal kriging with training images; 3.1 Choosing for random function theory or not?; 3.2 Formulation of universal kriging with training images; 3.2.1 Zero error-sum condition; 3.2.2 Minimum sum of square error condition; 3.3 Positive definiteness of the sop matrix; 3.4 Simple kriging with training images; 3.5 Creating a map of estimates; 3.6 Effect of the size of the training image; 3.7 Effect of the nature of the training image; 3.8 Training images for nonstationary modeling 3.9 Spatial estimation with nonstationary training images3.10 Summary of methodological differences; References; 4 Stochastic simulations based on random function theory; 4.1 The goal of stochastic simulations; 4.2 Stochastic simulation: Gaussian theory; 4.3 The sequential Gaussian simulation algorithm; 4.4 Properties of multi-Gaussian realizations; 4.5 Beyond Gaussian or beyond covariance?; References; 5 Stochastic simulation without random function theory; 5.1 Direct sampling; 5.1.1 Relying on information theory; 5.1.2 Application of direct sampling to Walker Lake 5.2 The extended normal equation5.2.1 Formulation; 5.2.2 The RAM solution; 5.2.3 Single normal equations simulation for Walker Lake; 5.2.4 The problem of conditioning; 5.3 Simulation by texture synthesis; 5.3.1 Computer graphics; 5.3.2 Image quilting; References; 6 Returning to the Sierra Nevada; Reference; Part II Methods; 1 Introduction; 2 The algorithmic building blocks; 2.1 Grid and pointset representations; 2.2 Multivariate grids; 2.3 Neighborhoods; 2.4 Storage and restitution of data events; 2.4.1 Raw storage of training image; 2.4.2 Cross-correlation based convolution 2.4.3 Partial convolution2.4.4 Tree storage; 2.4.5 List storage; 2.4.6 Clustering of patterns; 2.4.7 Parametric representation of patterns; 2.5 Computing distances; 2.5.1 Norms; 2.5.2 Hausdorff distance; 2.5.3 Invariant distances; 2.5.4 Change of variable; 2.5.5 Distances between distributions; 2.6 Sequential simulation; 2.6.1 Random path; 2.6.2 Unilateral path; 2.6.3 Patch-based methods; 2.6.4 Patch carving; 2.7 Multiple grids; 2.8 Conditioning; 2.8.1 The different types of data; 2.8.2 Different types of data: an example; 2.8.3 Steering proportions; References 3 Multiple-point geostatistics algorithms |
| Record Nr. | UNINA-9910140497903321 |
|
Mariethoz Gregoire
|
||
| Chichester, England ; ; Oxford, England ; ; Hoboken, New Jersey : , : Wiley Blackwell, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Multiple-point geostatistics : stochastic modeling with training images / / Gregoire Mariethoz and Jef Caers
| Multiple-point geostatistics : stochastic modeling with training images / / Gregoire Mariethoz and Jef Caers |
| Autore | Mariethoz Gregoire |
| Pubbl/distr/stampa | Chichester, England ; ; Oxford, England ; ; Hoboken, New Jersey : , : Wiley Blackwell, , 2015 |
| Descrizione fisica | 1 online resource (379 p.) |
| Disciplina | 551.01/5195 |
| Soggetto topico |
Geology - Statistical methods
Geological modeling |
| ISBN |
1-118-66293-8
1-118-66295-4 1-118-66294-6 |
| Classificazione | SCI031000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Multiple-point geostatistics; Contents; Preface; Acknowledgments; Part I Concepts; 1 Hiking in the Sierra Nevada; 1.1 An imaginary outdoor adventure company: Buena Sierra; 1.2 What lies ahead; 2 Spatial estimation based on random function theory; 2.1 Assumptions of stationarity; 2.2 Assumption of stationarity in spatial problems; 2.3 The kriging solution; 2.3.1 Unbiasedness condition; 2.3.2 Minimizing squared loss; 2.4 Estimating covariances; 2.5 Semivariogram modeling; 2.6 Using a limited neighborhood; 2.7 Universal kriging; 2.8 Semivariogram modeling for universal kriging
2.9 Simple trend example case2.10 Nonstationary covariances; 2.11 Assessment; References; 3 Universal kriging with training images; 3.1 Choosing for random function theory or not?; 3.2 Formulation of universal kriging with training images; 3.2.1 Zero error-sum condition; 3.2.2 Minimum sum of square error condition; 3.3 Positive definiteness of the sop matrix; 3.4 Simple kriging with training images; 3.5 Creating a map of estimates; 3.6 Effect of the size of the training image; 3.7 Effect of the nature of the training image; 3.8 Training images for nonstationary modeling 3.9 Spatial estimation with nonstationary training images3.10 Summary of methodological differences; References; 4 Stochastic simulations based on random function theory; 4.1 The goal of stochastic simulations; 4.2 Stochastic simulation: Gaussian theory; 4.3 The sequential Gaussian simulation algorithm; 4.4 Properties of multi-Gaussian realizations; 4.5 Beyond Gaussian or beyond covariance?; References; 5 Stochastic simulation without random function theory; 5.1 Direct sampling; 5.1.1 Relying on information theory; 5.1.2 Application of direct sampling to Walker Lake 5.2 The extended normal equation5.2.1 Formulation; 5.2.2 The RAM solution; 5.2.3 Single normal equations simulation for Walker Lake; 5.2.4 The problem of conditioning; 5.3 Simulation by texture synthesis; 5.3.1 Computer graphics; 5.3.2 Image quilting; References; 6 Returning to the Sierra Nevada; Reference; Part II Methods; 1 Introduction; 2 The algorithmic building blocks; 2.1 Grid and pointset representations; 2.2 Multivariate grids; 2.3 Neighborhoods; 2.4 Storage and restitution of data events; 2.4.1 Raw storage of training image; 2.4.2 Cross-correlation based convolution 2.4.3 Partial convolution2.4.4 Tree storage; 2.4.5 List storage; 2.4.6 Clustering of patterns; 2.4.7 Parametric representation of patterns; 2.5 Computing distances; 2.5.1 Norms; 2.5.2 Hausdorff distance; 2.5.3 Invariant distances; 2.5.4 Change of variable; 2.5.5 Distances between distributions; 2.6 Sequential simulation; 2.6.1 Random path; 2.6.2 Unilateral path; 2.6.3 Patch-based methods; 2.6.4 Patch carving; 2.7 Multiple grids; 2.8 Conditioning; 2.8.1 The different types of data; 2.8.2 Different types of data: an example; 2.8.3 Steering proportions; References 3 Multiple-point geostatistics algorithms |
| Record Nr. | UNINA-9910812133303321 |
|
Mariethoz Gregoire
|
||
| Chichester, England ; ; Oxford, England ; ; Hoboken, New Jersey : , : Wiley Blackwell, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Spatial and spatio-temporal geostatistical modeling and kriging / / José-María Montero, Department of Statistics, University of Castilla-La Mancha, Spain, Gema Fernández-Aviles, Department of Statistics, University of Castilla-La Mancha, Spain, Jorge Mateu, Department of Mathematics, University Jaume I of Castellon, Spain
| Spatial and spatio-temporal geostatistical modeling and kriging / / José-María Montero, Department of Statistics, University of Castilla-La Mancha, Spain, Gema Fernández-Aviles, Department of Statistics, University of Castilla-La Mancha, Spain, Jorge Mateu, Department of Mathematics, University Jaume I of Castellon, Spain |
| Autore | Montero José María |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Chichester, West Sussex, UK : , : John Wiley and Sons, Inc., , 2015 |
| Descrizione fisica | 1 online resource |
| Disciplina | 551.01/5195 |
| Altri autori (Persone) |
Fernández-AvilésGema
MateuJorge |
| Collana | Wiley Series in Probability and Statistics |
| Soggetto topico |
Geology - Statistical methods
Kriging |
| ISBN |
1-118-76238-X
1-118-76243-6 1-118-76242-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title Page -- Copyright -- Dedication -- Contents -- Foreword by Abdel H. El-Shaarawi -- Foreword by Hao Zhang -- List of figures -- List of tables -- About the companion website -- Chapter 1 From classical statistics to geostatistics -- 1.1 Not all spatial data are geostatistical data -- 1.2 The limits of classical statistics -- 1.3 A real geostatistical dataset: data on carbon monoxide in Madrid, Spain -- Chapter 2 Geostatistics: preliminaries -- 2.1 Regionalized variables -- 2.2 Random functions -- 2.3 Stationary and intrinsic hypotheses -- 2.3.1 Stationarity -- 2.3.2 Stationary random functions in the strict sense -- 2.3.3 Second-order stationary random functions -- 2.3.4 Intrinsically stationary random functions -- 2.3.5 Non-stationary random functions -- 2.4 Support -- Chapter 3 Structural analysis -- 3.1 Introduction -- 3.2 Covariance function -- 3.2.1 Definition and properties -- 3.2.2 Some theoretical isotropic covariance functions -- 3.3 Empirical covariogram -- 3.4 Semivariogram -- 3.4.1 Definition and properties -- 3.4.2 Behavior at intermediate and large distances -- 3.4.3 Behavior near the origin -- 3.4.4 A discontinuity at the origin -- 3.5 Theoretical semivariogram models -- 3.5.1 Semivariograms with a sill -- 3.5.2 Semivariograms with a hole effect -- 3.5.3 Semivariograms without a sill -- 3.5.4 Combining semivariogram models -- 3.6 Empirical semivariogram -- 3.7 Anisotropy -- 3.8 Fitting a semivariogram model -- 3.8.1 Manual fitting -- 3.8.2 Automatic fitting -- Chapter 4 Spatial prediction and kriging -- 4.1 Introduction -- 4.2 Neighborhood -- 4.3 Ordinary kriging -- 4.3.1 Point observation support and point predictor -- 4.3.2 Effects of a change in the model parameters -- 4.3.3 Point observation support and block predictor -- 4.3.4 Block observation support and block predictor.
4.4 Simple kriging: the special case of known mean -- 4.5 Simple kriging with an estimated mean -- 4.6 Universal kriging -- 4.6.1 Point observation support and point predictor -- 4.6.2 Point observation support and block predictor -- 4.6.3 Block observation support and block predictor -- 4.6.4 Kriging and exact interpolation -- 4.7 Residual kriging -- 4.7.1 Direct residual kriging -- 4.7.2 Iterative residual kriging -- 4.7.3 Modified iterative residual kriging -- 4.8 Median-Polish kriging -- 4.9 Cross-validation -- 4.10 Non-linear kriging -- 4.10.1 Disjunctive kriging -- 4.10.2 Indicator kriging -- Chapter 5 Geostatistics and spatio-temporal random functions -- 5.1 Spatio-temporal geostatistics -- 5.2 Spatio-temporal continuity -- 5.3 Relevant spatio-temporal concepts -- 5.4 Properties of the spatio-temporal covariance and semivariogram -- Chapter 6 Spatio-temporal structural analysis (I): empirical semivariogram and covariogram estimation and model fitting -- 6.1 Introduction -- 6.2 The empirical spatio-temporal semivariogram and covariogram -- 6.3 Fitting spatio-temporal semivariogram and covariogram models -- 6.4 Validation and comparison of spatio-temporal semivariogram and covariogram models -- Chapter 7 Spatio-temporal structural analysis (II): theoretical covariance models -- 7.1 Introduction -- 7.2 Combined distance or metric model -- 7.3 Sum model -- 7.4 Combined metric-sum model -- 7.5 Product model -- 7.6 Product-sum model -- 7.7 Porcu and Mateu mixture-based models -- 7.8 General product-sum model -- 7.9 Integrated product and product-sum models -- 7.10 Models proposed by Cressie and Huang -- 7.11 Models proposed by Gneiting -- 7.12 Mixture models proposed by Ma -- 7.12.1 Covariance functions generated by scale mixtures -- 7.12.2 Covariance functions generated by positive power mixtures. 7.13 Models generated by linear combinations proposed by Ma -- 7.14 Models proposed by Stein -- 7.15 Construction of covariance functions using copulas and completely monotonic functions -- 7.16 Generalized product-sum model -- 7.17 Models that are not fully symmetric -- 7.18 Mixture-based Bernstein zonally anisotropic covariance functions -- 7.19 Non-stationary models -- 7.19.1 Mixture of locally orthogonal stationary processes -- 7.19.2 Non-stationary models proposed by Ma -- 7.19.3 Non-stationary models proposed by Porcu and Mateu -- 7.20 Anisotropic covariance functions by Porcu and Mateu -- 7.20.1 Constructing temporally symmetric and spatially anisotropic covariance functions -- 7.20.2 Generalizing the class of spatio-temporal covariance functions proposed by Gneiting -- 7.20.3 Differentiation and integration operators acting on classes of anisotropic covariance functions on the basis of isotropic components: 'La descente étendue' -- 7.21 Spatio-temporal constructions based on quasi-arithmetic means of covariance functions -- 7.21.1 Multivariate quasi-arithmetic compositions -- 7.21.2 Permissibility criteria for quasi-arithmetic means of covariance functions on Rd -- 7.21.3 The use of quasi-arithmetic functionals to build non-separable, stationary, spatio-temporal covariance functions -- 7.21.4 Quasi-arithmeticity and non-stationarity in space -- Chapter 8 Spatio-temporal prediction and kriging -- 8.1 Spatio-temporal kriging -- 8.2 Spatio-temporal kriging equations -- Chapter 9 An introduction to functional geostatistics -- 9.1 Functional data analysis -- 9.2 Functional geostatistics: The parametric vs. the non-parametric approach -- 9.3 Functional ordinary kriging -- 9.3.1 Preliminaries -- 9.3.2 Functional ordinary kriging equations -- 9.3.3 Estimating the trace-semivariogram -- 9.3.4 Functional cross-validation -- Appendices. Appendix A Spectral representations -- A.1 Spectral representation of the covariogram -- A.2 Spectral representation of the semivariogram -- Appendix B Probabilistic aspects of Uij=Z(si)-Z(sj) -- Appendix C Basic theory on restricted maximum likelihood -- C.1 Restricted Maximum Likelihood equation -- Appendix D Most relevant proofs -- D.1 Product model: Peculiarity (ii) (Rodríguez-Iturbe and Mejia 1974 -- De Cesare et al. 1997) -- D.2 Product model: Peculiarity (iv) (Rodríguez-Iturbe and Mejia 1974 -- De Cesare et al. 1997) -- D.3 Product-sum model: Semivariogram expression (7.29) (De Iaco et al. 2001) -- D.4 General product-sum model: Obtaining the constant k (De Iaco et al. 2001) -- D.5 General product-sum model: Theorem 7.8.1 (De Iaco et al. 2001) -- D.6 General product-sum model: Theorem 7.8.2. (De Iaco et al. 2001) -- D.7 Generalized product-sum model. Proposition 1 1 (Gregori et al. 2008) -- D.8 Generalized product-sum model. Proposition 1 2 for n = 2 (Gregori et al. 2008) -- D.9 Generalized product-sum model. Corollary 1 3 of Proposition 2 (Gregori et al. 2008) -- D.10 Generalized product-sum model. Range of θ. Case 1: The Gaussian case 4 (Gregori et al. 2008) -- D.11 Generalized product-sum model. Range of θ. Case 2: The Matérn case 5 (Gregori et al. 2008) -- D.12 Generalized product-sum model. Range of θ. Case 3: The Gaussian-Matérn case 6 (Gregori et al. 2008) -- D.13 Mixture-based Bernstein zonally anisotropic covariance functions. Theorem 7.18.1 (Ma 2003b) -- D.14 Construction of non-stationary spatio-temporal covariance functions using spatio-temporal stationary covariances and intrinsically stationary semivariograms. Equation (7.159) (Ma 2003c). D.15 Construction of non-stationary spatio-temporal covariance functions using spatio-temporal stationary covariances and intrinsically stationary semivariograms. Equation (7.161) is a valid covariance function (Ma 2003c) -- D.16 Construction of non-stationary spatio-temporal covariance functions using spatio-temporal stationary covariances and intrinsically stationary semivariograms. Equation (7.163) Ma (2003c) -- D.17 Permissibility criteria for quasi-arithmetic means of covariance functions. Proposition 1 (Porcu et al. 2009b) -- Bibliography and further reading -- Index -- Supplemental Images -- Wiley Series in Probability and Statistics -- EULA. |
| Record Nr. | UNINA-9910208951203321 |
|
Montero José María
|
||
| Chichester, West Sussex, UK : , : John Wiley and Sons, Inc., , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Spatial and spatio-temporal geostatistical modeling and kriging / / José-María Montero, Department of Statistics, University of Castilla-La Mancha, Spain, Gema Fernández-Aviles, Department of Statistics, University of Castilla-La Mancha, Spain, Jorge Mateu, Department of Mathematics, University Jaume I of Castellon, Spain
| Spatial and spatio-temporal geostatistical modeling and kriging / / José-María Montero, Department of Statistics, University of Castilla-La Mancha, Spain, Gema Fernández-Aviles, Department of Statistics, University of Castilla-La Mancha, Spain, Jorge Mateu, Department of Mathematics, University Jaume I of Castellon, Spain |
| Autore | Montero José María |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Chichester, West Sussex, UK : , : John Wiley and Sons, Inc., , 2015 |
| Descrizione fisica | 1 online resource |
| Disciplina | 551.01/5195 |
| Altri autori (Persone) |
Fernández-AvilésGema
MateuJorge |
| Collana | Wiley Series in Probability and Statistics |
| Soggetto topico |
Geology - Statistical methods
Kriging |
| ISBN |
1-118-76238-X
1-118-76243-6 1-118-76242-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title Page -- Copyright -- Dedication -- Contents -- Foreword by Abdel H. El-Shaarawi -- Foreword by Hao Zhang -- List of figures -- List of tables -- About the companion website -- Chapter 1 From classical statistics to geostatistics -- 1.1 Not all spatial data are geostatistical data -- 1.2 The limits of classical statistics -- 1.3 A real geostatistical dataset: data on carbon monoxide in Madrid, Spain -- Chapter 2 Geostatistics: preliminaries -- 2.1 Regionalized variables -- 2.2 Random functions -- 2.3 Stationary and intrinsic hypotheses -- 2.3.1 Stationarity -- 2.3.2 Stationary random functions in the strict sense -- 2.3.3 Second-order stationary random functions -- 2.3.4 Intrinsically stationary random functions -- 2.3.5 Non-stationary random functions -- 2.4 Support -- Chapter 3 Structural analysis -- 3.1 Introduction -- 3.2 Covariance function -- 3.2.1 Definition and properties -- 3.2.2 Some theoretical isotropic covariance functions -- 3.3 Empirical covariogram -- 3.4 Semivariogram -- 3.4.1 Definition and properties -- 3.4.2 Behavior at intermediate and large distances -- 3.4.3 Behavior near the origin -- 3.4.4 A discontinuity at the origin -- 3.5 Theoretical semivariogram models -- 3.5.1 Semivariograms with a sill -- 3.5.2 Semivariograms with a hole effect -- 3.5.3 Semivariograms without a sill -- 3.5.4 Combining semivariogram models -- 3.6 Empirical semivariogram -- 3.7 Anisotropy -- 3.8 Fitting a semivariogram model -- 3.8.1 Manual fitting -- 3.8.2 Automatic fitting -- Chapter 4 Spatial prediction and kriging -- 4.1 Introduction -- 4.2 Neighborhood -- 4.3 Ordinary kriging -- 4.3.1 Point observation support and point predictor -- 4.3.2 Effects of a change in the model parameters -- 4.3.3 Point observation support and block predictor -- 4.3.4 Block observation support and block predictor.
4.4 Simple kriging: the special case of known mean -- 4.5 Simple kriging with an estimated mean -- 4.6 Universal kriging -- 4.6.1 Point observation support and point predictor -- 4.6.2 Point observation support and block predictor -- 4.6.3 Block observation support and block predictor -- 4.6.4 Kriging and exact interpolation -- 4.7 Residual kriging -- 4.7.1 Direct residual kriging -- 4.7.2 Iterative residual kriging -- 4.7.3 Modified iterative residual kriging -- 4.8 Median-Polish kriging -- 4.9 Cross-validation -- 4.10 Non-linear kriging -- 4.10.1 Disjunctive kriging -- 4.10.2 Indicator kriging -- Chapter 5 Geostatistics and spatio-temporal random functions -- 5.1 Spatio-temporal geostatistics -- 5.2 Spatio-temporal continuity -- 5.3 Relevant spatio-temporal concepts -- 5.4 Properties of the spatio-temporal covariance and semivariogram -- Chapter 6 Spatio-temporal structural analysis (I): empirical semivariogram and covariogram estimation and model fitting -- 6.1 Introduction -- 6.2 The empirical spatio-temporal semivariogram and covariogram -- 6.3 Fitting spatio-temporal semivariogram and covariogram models -- 6.4 Validation and comparison of spatio-temporal semivariogram and covariogram models -- Chapter 7 Spatio-temporal structural analysis (II): theoretical covariance models -- 7.1 Introduction -- 7.2 Combined distance or metric model -- 7.3 Sum model -- 7.4 Combined metric-sum model -- 7.5 Product model -- 7.6 Product-sum model -- 7.7 Porcu and Mateu mixture-based models -- 7.8 General product-sum model -- 7.9 Integrated product and product-sum models -- 7.10 Models proposed by Cressie and Huang -- 7.11 Models proposed by Gneiting -- 7.12 Mixture models proposed by Ma -- 7.12.1 Covariance functions generated by scale mixtures -- 7.12.2 Covariance functions generated by positive power mixtures. 7.13 Models generated by linear combinations proposed by Ma -- 7.14 Models proposed by Stein -- 7.15 Construction of covariance functions using copulas and completely monotonic functions -- 7.16 Generalized product-sum model -- 7.17 Models that are not fully symmetric -- 7.18 Mixture-based Bernstein zonally anisotropic covariance functions -- 7.19 Non-stationary models -- 7.19.1 Mixture of locally orthogonal stationary processes -- 7.19.2 Non-stationary models proposed by Ma -- 7.19.3 Non-stationary models proposed by Porcu and Mateu -- 7.20 Anisotropic covariance functions by Porcu and Mateu -- 7.20.1 Constructing temporally symmetric and spatially anisotropic covariance functions -- 7.20.2 Generalizing the class of spatio-temporal covariance functions proposed by Gneiting -- 7.20.3 Differentiation and integration operators acting on classes of anisotropic covariance functions on the basis of isotropic components: 'La descente étendue' -- 7.21 Spatio-temporal constructions based on quasi-arithmetic means of covariance functions -- 7.21.1 Multivariate quasi-arithmetic compositions -- 7.21.2 Permissibility criteria for quasi-arithmetic means of covariance functions on Rd -- 7.21.3 The use of quasi-arithmetic functionals to build non-separable, stationary, spatio-temporal covariance functions -- 7.21.4 Quasi-arithmeticity and non-stationarity in space -- Chapter 8 Spatio-temporal prediction and kriging -- 8.1 Spatio-temporal kriging -- 8.2 Spatio-temporal kriging equations -- Chapter 9 An introduction to functional geostatistics -- 9.1 Functional data analysis -- 9.2 Functional geostatistics: The parametric vs. the non-parametric approach -- 9.3 Functional ordinary kriging -- 9.3.1 Preliminaries -- 9.3.2 Functional ordinary kriging equations -- 9.3.3 Estimating the trace-semivariogram -- 9.3.4 Functional cross-validation -- Appendices. Appendix A Spectral representations -- A.1 Spectral representation of the covariogram -- A.2 Spectral representation of the semivariogram -- Appendix B Probabilistic aspects of Uij=Z(si)-Z(sj) -- Appendix C Basic theory on restricted maximum likelihood -- C.1 Restricted Maximum Likelihood equation -- Appendix D Most relevant proofs -- D.1 Product model: Peculiarity (ii) (Rodríguez-Iturbe and Mejia 1974 -- De Cesare et al. 1997) -- D.2 Product model: Peculiarity (iv) (Rodríguez-Iturbe and Mejia 1974 -- De Cesare et al. 1997) -- D.3 Product-sum model: Semivariogram expression (7.29) (De Iaco et al. 2001) -- D.4 General product-sum model: Obtaining the constant k (De Iaco et al. 2001) -- D.5 General product-sum model: Theorem 7.8.1 (De Iaco et al. 2001) -- D.6 General product-sum model: Theorem 7.8.2. (De Iaco et al. 2001) -- D.7 Generalized product-sum model. Proposition 1 1 (Gregori et al. 2008) -- D.8 Generalized product-sum model. Proposition 1 2 for n = 2 (Gregori et al. 2008) -- D.9 Generalized product-sum model. Corollary 1 3 of Proposition 2 (Gregori et al. 2008) -- D.10 Generalized product-sum model. Range of θ. Case 1: The Gaussian case 4 (Gregori et al. 2008) -- D.11 Generalized product-sum model. Range of θ. Case 2: The Matérn case 5 (Gregori et al. 2008) -- D.12 Generalized product-sum model. Range of θ. Case 3: The Gaussian-Matérn case 6 (Gregori et al. 2008) -- D.13 Mixture-based Bernstein zonally anisotropic covariance functions. Theorem 7.18.1 (Ma 2003b) -- D.14 Construction of non-stationary spatio-temporal covariance functions using spatio-temporal stationary covariances and intrinsically stationary semivariograms. Equation (7.159) (Ma 2003c). D.15 Construction of non-stationary spatio-temporal covariance functions using spatio-temporal stationary covariances and intrinsically stationary semivariograms. Equation (7.161) is a valid covariance function (Ma 2003c) -- D.16 Construction of non-stationary spatio-temporal covariance functions using spatio-temporal stationary covariances and intrinsically stationary semivariograms. Equation (7.163) Ma (2003c) -- D.17 Permissibility criteria for quasi-arithmetic means of covariance functions. Proposition 1 (Porcu et al. 2009b) -- Bibliography and further reading -- Index -- Supplemental Images -- Wiley Series in Probability and Statistics -- EULA. |
| Record Nr. | UNINA-9910806919403321 |
|
Montero José María
|
||
| Chichester, West Sussex, UK : , : John Wiley and Sons, Inc., , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||