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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 | ||
| ||