New advances in space-time random field modelling:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Castelló de la Plana
Universitat Jaume I
c2008
|
| Series: | Col·lecció "Treballs d'informàtica i tecnologia"
núm. 28 ; 28 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiv, 319 Seiten Illustrationen, Diagramme 24 cm |
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Record in the Search Index
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| adam_text | Contents 1 Introduction 1.1 1.2 1.3 1 Preludium............................................................................ Spatial statistics ............................................................... Theoretical background...................................................... 1.3.1 Symbols and notation ........................................... 1.3.2 Space-time geostatistics ........................................ 1 З 9 9 10 I New Classes of Space-Time Covariance Func tions 13 2 New classes of covariance and spectral density functions for spatio-temporal modelling 15 2.1 2.2 2.3 2.4 2.5 3 Introduction........................................................................ Building spatio-temporalcovariance functions................................................................................ 2.2.1 Particular examples................................................. Building spatio-temporal models through the spectral density function............................... 2.3.1 Particular examples................................................. An application to wind speed data ................................. Conclusions and discussion................................................ 18 22 24 29 33 35 42 Modelling spatio-temporal data: a new variogram and covariance structure proposal 45 3.1 3.2 Introduction........................................................................ The Dagum spatio-temporal covariance and variogram . i 45 47
3.3 Conclusions and discussion................................................. 52 4 Decoupling the local and global behaviour: the Dagum Random Field case 55 Introduction.......................................................................... The Dagum class of correlation functions for isotropic RF 4.2.1 Prolegomena: the Dagum function ..................... 4.2.2 The Dagum correlation function and related models 4.3 Local and global behaviour of the Dagum RF ................................................................. 61 4.4 Simulation study................................................................. 4.4.1 Profiles....................................................................... 4.4.2 Surfaces.................................................................... 4.5 Conclusions and discussion.................................................. 4.1 4.2 56 59 59 59 63 63 66 70 5 Nonseparable stationary anisotropic space-time covari ance functions 75 5.1 Introduction.......................................................................... 75 5.2 Background and main results ............................................ 77 5.2.1 Anisotropy throughisotropy between components 77 5.2.2 Direct construction:partitioning the spatial domain 78 5.3 Connections with previously proposed models................ 82 5.4 Examples............................................................................. 86 5.5 Conclusions and discussion.................................................. 88 6 Covariance functions which are stationary or nonstationary in space and stationary in
time 95 6.1 6.2 6.3 Introduction.......................................................................... 96 The Bernstein class of stationary space-time covariance functions....................................................................... 97 6.2.1 Differential operators preserving positive definite ness of Bernsteinclass............................................ 102 6.2.2 Examples.................................................................. 106 Temporally stationary and spatially nonstationary covariances ........................................ 110 6.3.1 Examples.................................................................. 112 ii
6.4 6.5 Irish wind speed data: detecting anisotropy.................................................................... 113 Conclusions and discussion................................................. 119 7 Archimedean spectral densities for nonstationary space time Geostatistics 123 7.1 7.2 7.3 7.4 7.5 II Introduction andsetup.......................................................... 124 Methodology: Archimedean composition of two real func tions ............................................................................... 127 7.2.1 Orderingrelations for Archimedean compositions 128 Nonstationary covariance functions via Archimedean spa tial adaptation of parametric spectra...................... 130 7.3.1 Archimedean spectral densities ............................ 130 7.3.2 Nonstationary Archimedean spectral densities for spatial data............................................................. 131 Archimedean spatially adaptivetemporally adaptive and asymmetric covariances ................................................................. 136 Conclusions and discussion................................................. 138 Linear Operators on the Space-Time Domain 139 8 La descente et la montée étendues: the spatially d-anisotropic and the spatio-temporal case 141 8.1 8.2 8.3 8.4 8.5 Introduction......................................................................... Background, definitions and characterisations ............... Descendre............................................................................ 8.3.1 Working with some particular classes of correlation
functions....................................................... 151 8.3.2 Ne pas descendre. Not always differentiation means descendre.................................................... 155 Monter.................................................................................. Conclusions and discussion................................................ 9 Quasi-arithmetic means of covariance functions with po tential applications to space-time data 163 iii 142 143 148 156 159
Introduction.......................................................................... Background and methodology........................................... 9.2.1 Covariance functions: recalling some characterisa tion and basic properties............................ 166 9.2.2 The methodology. Quasi-arithmetic multivariate compositions .............................................. 169 9.3 Theoretical results .............................................................. 9.4 Using quasi-arithmetic functionals in theconstruction of nonseparable space-time covariancefunctions.................... 9.4.1 On the representation and smoothness properties of QARF ................................................................ 9.4.2 Applications of quasi-arithmeticity in the construction of stationary nonseparable space-time covariances ................................................. 180 9.4.3 Quasi-arithmeticity and nonstationarity in space....................................................... 183 9.5 Conclusions anddiscussion.................................................. 9.1 9.2 164 166 173 177 177 186 10 On potentially negative space-time covariances obtained as sum of productsof marginal ones 189 10.1 Introduction......................................................................... 190 10.2 Main results......................................................................... 191 10.2.1 The Generalised Sum-of-Products model and its negative covariances...................... 191 10.2.2 The Generalised Product-Sum model: a caution ary
example................................................. 198 10.2.3 Variograms through particular linear combinations of Bernstein functions with negative weights . . . 201 10.3 Conclusions and discussion................................................. 205 11 Some applications to real data 209 11.1 Introduction.......................................................................... 210 11.2 Statistical modelling of Indian Ocean wind speed data . . 212 11.2.1 The data and the statistical problem................... 212 11.2.2 Estimation and fitting........................................... 214 11.2.3 Diagnostica and interpolation............................... 217 iv
11.3 Statistical modelling of the geothermal field of Nea Kessani, Greece.......................................................................... 222 11.3.1 Geology of the studyarea..................................... 11.3.2 Drill-hole data......................................................... 11.3.3 Motivation............................................................... 11.3.4 Exploratory analysis............................................. 11.3.5 Data analysis and diagnostics.............................. 11.4 Conclusions and discussion................................................. III Nonparametric Space-Time Geostatistics 222 223 223 224 225 229 237 12 A kernel-based method for nonparametric estimation of variograms 239 12.1 Introduction........................................................................ 241 12.2 Classical variogram setup................................................... 242 12.3 Extensions to the variogram estimator .......................... 243 12.4 Simulation study............................................................... 248 12.5 Data set analysis: revisitedcases ..................................... 256 12.5.1 Wolfcamp-Aquiferdata set...................................... 257 12.5.2 Coal-ash data set.................................................... 259 12.6 Conclusions and discussion................................................ 264 13 Spatial and spatio-temporal dependence of the periodogram for regularly spaced data 273 13.1 Introduction........................................................................ 274 13.2
Background and setup...................................................... 276 13.2.1 Spatial framework.................................................... 276 13.2.2 Spatio-temporal framework .................................. 279 13.2.3 Cumulants and spectral cumulants. Spatial and spatio-temporal cases.................................. 280 13.3 Main results........................................................................ 282 13.3.1 Theoretical results in thespatial domain.............. 282 13.3.2 Theoretical results in thespatio-temporal domain 289 13.4 Conclusions and discussion............................................... 293 v
IV 297 Bibliography 14 List of references 2θθ vi
|
| adam_txt |
Contents 1 Introduction 1.1 1.2 1.3 1 Preludium. Spatial statistics . Theoretical background. 1.3.1 Symbols and notation . 1.3.2 Space-time geostatistics . 1 З 9 9 10 I New Classes of Space-Time Covariance Func tions 13 2 New classes of covariance and spectral density functions for spatio-temporal modelling 15 2.1 2.2 2.3 2.4 2.5 3 Introduction. Building spatio-temporalcovariance functions. 2.2.1 Particular examples. Building spatio-temporal models through the spectral density function. 2.3.1 Particular examples. An application to wind speed data . Conclusions and discussion. 18 22 24 29 33 35 42 Modelling spatio-temporal data: a new variogram and covariance structure proposal 45 3.1 3.2 Introduction. The Dagum spatio-temporal covariance and variogram . i 45 47
3.3 Conclusions and discussion. 52 4 Decoupling the local and global behaviour: the Dagum Random Field case 55 Introduction. The Dagum class of correlation functions for isotropic RF 4.2.1 Prolegomena: the Dagum function . 4.2.2 The Dagum correlation function and related models 4.3 Local and global behaviour of the Dagum RF . 61 4.4 Simulation study. 4.4.1 Profiles. 4.4.2 Surfaces. 4.5 Conclusions and discussion. 4.1 4.2 56 59 59 59 63 63 66 70 5 Nonseparable stationary anisotropic space-time covari ance functions 75 5.1 Introduction. 75 5.2 Background and main results . 77 5.2.1 Anisotropy throughisotropy between components 77 5.2.2 Direct construction:partitioning the spatial domain 78 5.3 Connections with previously proposed models. 82 5.4 Examples. 86 5.5 Conclusions and discussion. 88 6 Covariance functions which are stationary or nonstationary in space and stationary in
time 95 6.1 6.2 6.3 Introduction. 96 The Bernstein class of stationary space-time covariance functions. 97 6.2.1 Differential operators preserving positive definite ness of Bernsteinclass. 102 6.2.2 Examples. 106 Temporally stationary and spatially nonstationary covariances . 110 6.3.1 Examples. 112 ii
6.4 6.5 Irish wind speed data: detecting anisotropy. 113 Conclusions and discussion. 119 7 Archimedean spectral densities for nonstationary space time Geostatistics 123 7.1 7.2 7.3 7.4 7.5 II Introduction andsetup. 124 Methodology: Archimedean composition of two real func tions . 127 7.2.1 Orderingrelations for Archimedean compositions 128 Nonstationary covariance functions via Archimedean spa tial adaptation of parametric spectra. 130 7.3.1 Archimedean spectral densities . 130 7.3.2 Nonstationary Archimedean spectral densities for spatial data. 131 Archimedean spatially adaptivetemporally adaptive and asymmetric covariances . 136 Conclusions and discussion. 138 Linear Operators on the Space-Time Domain 139 8 La descente et la montée étendues: the spatially d-anisotropic and the spatio-temporal case 141 8.1 8.2 8.3 8.4 8.5 Introduction. Background, definitions and characterisations . Descendre. 8.3.1 Working with some particular classes of correlation
functions. 151 8.3.2 Ne pas descendre. Not always differentiation means descendre. 155 Monter. Conclusions and discussion. 9 Quasi-arithmetic means of covariance functions with po tential applications to space-time data 163 iii 142 143 148 156 159
Introduction. Background and methodology. 9.2.1 Covariance functions: recalling some characterisa tion and basic properties. 166 9.2.2 The methodology. Quasi-arithmetic multivariate compositions . 169 9.3 Theoretical results . 9.4 Using quasi-arithmetic functionals in theconstruction of nonseparable space-time covariancefunctions. 9.4.1 On the representation and smoothness properties of QARF . 9.4.2 Applications of quasi-arithmeticity in the construction of stationary nonseparable space-time covariances . 180 9.4.3 Quasi-arithmeticity and nonstationarity in space. 183 9.5 Conclusions anddiscussion. 9.1 9.2 164 166 173 177 177 186 10 On potentially negative space-time covariances obtained as sum of productsof marginal ones 189 10.1 Introduction. 190 10.2 Main results. 191 10.2.1 The Generalised Sum-of-Products model and its negative covariances. 191 10.2.2 The Generalised Product-Sum model: a caution ary
example. 198 10.2.3 Variograms through particular linear combinations of Bernstein functions with negative weights . . . 201 10.3 Conclusions and discussion. 205 11 Some applications to real data 209 11.1 Introduction. 210 11.2 Statistical modelling of Indian Ocean wind speed data . . 212 11.2.1 The data and the statistical problem. 212 11.2.2 Estimation and fitting. 214 11.2.3 Diagnostica and interpolation. 217 iv
11.3 Statistical modelling of the geothermal field of Nea Kessani, Greece. 222 11.3.1 Geology of the studyarea. 11.3.2 Drill-hole data. 11.3.3 Motivation. 11.3.4 Exploratory analysis. 11.3.5 Data analysis and diagnostics. 11.4 Conclusions and discussion. III Nonparametric Space-Time Geostatistics 222 223 223 224 225 229 237 12 A kernel-based method for nonparametric estimation of variograms 239 12.1 Introduction. 241 12.2 Classical variogram setup. 242 12.3 Extensions to the variogram estimator . 243 12.4 Simulation study. 248 12.5 Data set analysis: revisitedcases . 256 12.5.1 Wolfcamp-Aquiferdata set. 257 12.5.2 Coal-ash data set. 259 12.6 Conclusions and discussion. 264 13 Spatial and spatio-temporal dependence of the periodogram for regularly spaced data 273 13.1 Introduction. 274 13.2
Background and setup. 276 13.2.1 Spatial framework. 276 13.2.2 Spatio-temporal framework . 279 13.2.3 Cumulants and spectral cumulants. Spatial and spatio-temporal cases. 280 13.3 Main results. 282 13.3.1 Theoretical results in thespatial domain. 282 13.3.2 Theoretical results in thespatio-temporal domain 289 13.4 Conclusions and discussion. 293 v
IV 297 Bibliography 14 List of references 2θθ vi |
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| indexdate | 2024-07-10T09:41:34Z |
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| spelling | Porcu, Emilio ca. 20./21. Jh. Verfasser (DE-588)1274384788 aut New advances in space-time random field modelling Emilio Porcu, Jorge Mateu Castelló de la Plana Universitat Jaume I c2008 xiv, 319 Seiten Illustrationen, Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Col·lecció "Treballs d'informàtica i tecnologia" núm. 28 28 Spatial analysis (Statistics) Analyse spatiale (Statistique) spatial analysis aat Spatial analysis (Statistics) fast Zufälliges Feld (DE-588)4191094-1 gnd rswk-swf Räumliche Statistik (DE-588)4386767-4 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Zufälliges Feld (DE-588)4191094-1 s Stochastik (DE-588)4121729-9 s Räumliche Statistik (DE-588)4386767-4 s DE-604 Mateu, Jorge Sonstige (DE-588)111636865X oth Col·lecció "Treballs d'informàtica i tecnologia" núm. 28 ; 28 (DE-604)BV048592267 28 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033939137&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Porcu, Emilio ca. 20./21. Jh New advances in space-time random field modelling Col·lecció "Treballs d'informàtica i tecnologia" Spatial analysis (Statistics) Analyse spatiale (Statistique) spatial analysis aat Spatial analysis (Statistics) fast Zufälliges Feld (DE-588)4191094-1 gnd Räumliche Statistik (DE-588)4386767-4 gnd Stochastik (DE-588)4121729-9 gnd |
| subject_GND | (DE-588)4191094-1 (DE-588)4386767-4 (DE-588)4121729-9 |
| title | New advances in space-time random field modelling |
| title_auth | New advances in space-time random field modelling |
| title_exact_search | New advances in space-time random field modelling |
| title_exact_search_txtP | New advances in space-time random field modelling |
| title_full | New advances in space-time random field modelling Emilio Porcu, Jorge Mateu |
| title_fullStr | New advances in space-time random field modelling Emilio Porcu, Jorge Mateu |
| title_full_unstemmed | New advances in space-time random field modelling Emilio Porcu, Jorge Mateu |
| title_short | New advances in space-time random field modelling |
| title_sort | new advances in space time random field modelling |
| topic | Spatial analysis (Statistics) Analyse spatiale (Statistique) spatial analysis aat Spatial analysis (Statistics) fast Zufälliges Feld (DE-588)4191094-1 gnd Räumliche Statistik (DE-588)4386767-4 gnd Stochastik (DE-588)4121729-9 gnd |
| topic_facet | Spatial analysis (Statistics) Analyse spatiale (Statistique) spatial analysis Zufälliges Feld Räumliche Statistik Stochastik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033939137&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT porcuemilio newadvancesinspacetimerandomfieldmodelling AT mateujorge newadvancesinspacetimerandomfieldmodelling |