Model-based geostatistics:
This volume is the first book-length treatment of model-based geostatistics. The text is expository, emphasizing statistical methods and applications rather than the underlying mathematical theory. Analyses of datasets from a range of scientific contexts feature prominently, and simulations are used...
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2007
|
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Summary: | This volume is the first book-length treatment of model-based geostatistics. The text is expository, emphasizing statistical methods and applications rather than the underlying mathematical theory. Analyses of datasets from a range of scientific contexts feature prominently, and simulations are used to illustrate theoretical results. Readers can reproduce most of the computational results in the book by using the authors' software package, geoR, whose usage is illustrated in a computation section at the end of each chapter. The book assumes a working knowledge of classical and Bayesian methods of inference, linear models, and generalized linear models. |
| Physical Description: | XIII, 228 S. Ill., graph. Darst., Kt. |
| ISBN: | 0387329072 9780387329079 |
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| adam_text | Contents
Preface v
1 Introduction 1
1.1 Motivating examples 1
1.2 Terminology and notation 9
1.2.1 Support 9
1.2.2 Multivariate responses and explanatory variables . . 10
1.2.3 Sampling design 12
1.3 Scientific objectives 12
1.4 Generalised linear geostatistical models 13
1.5 What is in this book? 15
1.5.1 Organisation of the book 1G
1.5.2 Statistical pre requisites 17
1.6 Computation 17
1.6.1 Elevation data 17
1.6.2 More on the geodata object 20
1.6.3 Rongelap data 22
1.6.4 The Gambia malaria data 24
1.6.5 The soil data 24
1.7 Exercises 26
2 An overview of model based geostatistics 27
2.1 Design 27
2.2 Model formulation 28
2.3 Exploratory data analysis 30
2.3.1 Non spatial exploratory analysis 30
x Contents
2.3.2 Spatial exploratory analysis 31
2.4 The distinction between parameter estimation and spatial
prediction 35
2.5 Parameter estimation 36
2.6 Spatial prediction 37
2.7 Definitions of distance 39
2.8 Computation 40
2.9 Exercises 45
3 Gaussian models for geostatistical data 46
3.1 Covariance functions and the variogram 46
3.2 Regularisation 48
3.3 Continuity and differentiability of stochastic processes ... 49
3.4 Families of covariance functions and their properties 51
3.4.1 The Matern family 51
3.4.2 The powered exponential family 53
3.4.3 Other families 54
3.5 The nugget effect 56
3.6 Spatial trends 57
3.7 Directional effects 58
3.8 Transformed Gaussian models 60
3.9 Intrinsic models 63
3.10 Unconditional and conditional simulation 66
3.11 Low rank models 68
3.12 Multivariate models 69
3.12.1 Cross covariance, cross correlation and cross variogram 70
3.12.2 Bivariate signal and noise 71
3.12.3 Some simple constructions 72
3.13 Computation 74
3.14 Exercises 77
4 Generalized linear models for geostatistical data 79
4.1 General formulation 79
4.2 The approximate covariance function and variogram 81
4.3 Examples of generalised linear geostatistical models 82
4.3.1 The Poisson log linear model 82
4.3.2 The binomial logistic linear model 83
4.3.3 Spatial survival analysis 84
4.4 Point process models and geostatistics 86
4.4.1 Cox processes 87
4.4.2 Preferential sampling 89
4.5 Some examples of other model constructions 93
4.5.1 Scan processes 93
4.5.2 Random sets 94
4.6 Computation 94
4.6.1 Simulating from the generalised linear model 94
4.6.2 Preferential sampling 96
Contents xi
4.7 Exercises 97
5 Classical parameter estimation 99
5.1 Trend estimation 100
5.2 Variograms 100
5.2.1 The theoretical variogram 100
5.2.2 The empirical variogram 102
5.2.3 Smoothing the empirical variogram 102
5.2.4 Exploring directional effects 104
5.2.5 The interplay between trend and covariance structure 105
5.3 Curve fitting methods for estimating covariance structure . . 107
5.3.1 Ordinary least squares 108
5.3.2 Weighted least squares 108
5.3.3 Comments on curve fitting methods 110
5.4 Maximum likelihood estimation 112
5.4.1 General ideas 112
5.4.2 Gaussian models 112
5.4.3 Profile likelihood 114
5.4.4 Application to the surface elevation data 114
5.4.5 Restricted maximum likelihood estimation for the
Gaussian linear model 116
5.4.6 Trans Gaussian models 117
5.4.7 Analysis of Swiss rainfall data 118
5.4.8 Analysis of soil calcium data 121
5.5 Parameter estimation for generalized linear geostatistical
models 123
5.5.1 Monte Carlo maximum likelihood 124
5.5.2 Hierarchical likelihood 125
5.5.3 Generalized estimating equations 125
5.6 Computation 126
5.6.1 Variogram calculations 126
5.6.2 Parameter estimation 130
5.7 Exercises 132
6 Spatial prediction 134
6.1 Minimum mean square error prediction 134
6.2 Minimum mean square error prediction for the stationary
Gaussian model 136
6.2.1 Prediction of the signal at a point 136
6.2.2 Simple and ordinary kriging 137
6.2.3 Prediction of linear targets 138
6.2.4 Prediction of non linear targets 138
6.3 Prediction with a nugget effect 139
6.4 What does kriging actually do to the data? 140
6.4.1 The prediction weights 141
6.4.2 Varying the correlation parameter 144
6.4.3 Varying the noise to signal ratio 146
xii Contents
6.5 Trans Gaussian kriging 147
6.5.1 Analysis of Swiss rainfall data (continued) 149
6.6 Kriging with non constant mean 151
6.6.1 Analysis of soil calcium data (continued) 151
6.7 Computation 151
6.8 Exercises 155
7 Bayesian inference 157
7.1 The Bayesian paradigm: a unified treatment of estimation and
prediction 157
7.1.1 Prediction using plug in estimates 157
7.1.2 Bayesian prediction 158
7.1.3 Obstacles to practical Bayesian prediction 160
7.2 Bayesian estimation and prediction for the Gaussian linear
model 160
7.2.1 Estimation 161
7.2.2 Prediction when correlation parameters are known . 163
7.2.3 Uncertainty in the correlation parameters 164
7.2.4 Prediction of targets which depend on both the signal
and the spatial trend 165
7.3 Trans Gaussian models 166
7.4 Case studies 167
7.4.1 Surface elevations 167
7.4.2 Analysis of Swiss rainfall data (continued) 169
7.5 Bayesian estimation and prediction for generalized linear
geostatistical models 172
7.5.1 Markov chain Monte Carlo 172
7.5.2 Estimation 173
7.5.3 Prediction 176
7.5.4 Some possible improvements to the MCMC algorithm 177
7.6 Case studies in generalized linear geostatistical modelling . . 179
7.6.1 Simulated data 179
7.6.2 Rongelap island 181
7.6.3 Childhood malaria in The Gambia 185
7.6.4 Loa loa prevalence in equatorial Africa 187
7.7 Computation 193
7.7.1 Gaussian models 193
7.7.2 Non Gaussian models 196
7.8 Exercises 196
8 Geostatistical design 199
8.1 Choosing the study region 201
8.2 Choosing the sample locations: uniform designs 202
8.3 Designing for efficient prediction 203
8.4 Designing for efficient parameter estimation 204
8.5 A Bayesian design criterion 206
8.5.1 Retrospective design 206
Contents xiii
8.5.2 Prospective design 209
8.6 Exercises 211
A Statistical background 213
A.I Statistical models 213
A.2 Classical inference 213
A.3 Bayesian inference 215
A.4 Prediction 216
References 218
Index 227
|
| adam_txt |
Contents
Preface v
1 Introduction 1
1.1 Motivating examples 1
1.2 Terminology and notation 9
1.2.1 Support 9
1.2.2 Multivariate responses and explanatory variables . . 10
1.2.3 Sampling design 12
1.3 Scientific objectives 12
1.4 Generalised linear geostatistical models 13
1.5 What is in this book? 15
1.5.1 Organisation of the book 1G
1.5.2 Statistical pre requisites 17
1.6 Computation 17
1.6.1 Elevation data 17
1.6.2 More on the geodata object 20
1.6.3 Rongelap data 22
1.6.4 The Gambia malaria data 24
1.6.5 The soil data 24
1.7 Exercises 26
2 An overview of model based geostatistics 27
2.1 Design 27
2.2 Model formulation 28
2.3 Exploratory data analysis 30
2.3.1 Non spatial exploratory analysis 30
x Contents
2.3.2 Spatial exploratory analysis 31
2.4 The distinction between parameter estimation and spatial
prediction 35
2.5 Parameter estimation 36
2.6 Spatial prediction 37
2.7 Definitions of distance 39
2.8 Computation 40
2.9 Exercises 45
3 Gaussian models for geostatistical data 46
3.1 Covariance functions and the variogram 46
3.2 Regularisation 48
3.3 Continuity and differentiability of stochastic processes . 49
3.4 Families of covariance functions and their properties 51
3.4.1 The Matern family 51
3.4.2 The powered exponential family 53
3.4.3 Other families 54
3.5 The nugget effect 56
3.6 Spatial trends 57
3.7 Directional effects 58
3.8 Transformed Gaussian models 60
3.9 Intrinsic models 63
3.10 Unconditional and conditional simulation 66
3.11 Low rank models 68
3.12 Multivariate models 69
3.12.1 Cross covariance, cross correlation and cross variogram 70
3.12.2 Bivariate signal and noise 71
3.12.3 Some simple constructions 72
3.13 Computation 74
3.14 Exercises 77
4 Generalized linear models for geostatistical data 79
4.1 General formulation 79
4.2 The approximate covariance function and variogram 81
4.3 Examples of generalised linear geostatistical models 82
4.3.1 The Poisson log linear model 82
4.3.2 The binomial logistic linear model 83
4.3.3 Spatial survival analysis 84
4.4 Point process models and geostatistics 86
4.4.1 Cox processes 87
4.4.2 Preferential sampling 89
4.5 Some examples of other model constructions 93
4.5.1 Scan processes 93
4.5.2 Random sets 94
4.6 Computation 94
4.6.1 Simulating from the generalised linear model 94
4.6.2 Preferential sampling 96
Contents xi
4.7 Exercises 97
5 Classical parameter estimation 99
5.1 Trend estimation 100
5.2 Variograms 100
5.2.1 The theoretical variogram 100
5.2.2 The empirical variogram 102
5.2.3 Smoothing the empirical variogram 102
5.2.4 Exploring directional effects 104
5.2.5 The interplay between trend and covariance structure 105
5.3 Curve fitting methods for estimating covariance structure . . 107
5.3.1 Ordinary least squares 108
5.3.2 Weighted least squares 108
5.3.3 Comments on curve fitting methods 110
5.4 Maximum likelihood estimation 112
5.4.1 General ideas 112
5.4.2 Gaussian models 112
5.4.3 Profile likelihood 114
5.4.4 Application to the surface elevation data 114
5.4.5 Restricted maximum likelihood estimation for the
Gaussian linear model 116
5.4.6 Trans Gaussian models 117
5.4.7 Analysis of Swiss rainfall data 118
5.4.8 Analysis of soil calcium data 121
5.5 Parameter estimation for generalized linear geostatistical
models 123
5.5.1 Monte Carlo maximum likelihood 124
5.5.2 Hierarchical likelihood 125
5.5.3 Generalized estimating equations 125
5.6 Computation 126
5.6.1 Variogram calculations 126
5.6.2 Parameter estimation 130
5.7 Exercises 132
6 Spatial prediction 134
6.1 Minimum mean square error prediction 134
6.2 Minimum mean square error prediction for the stationary
Gaussian model 136
6.2.1 Prediction of the signal at a point 136
6.2.2 Simple and ordinary kriging 137
6.2.3 Prediction of linear targets 138
6.2.4 Prediction of non linear targets 138
6.3 Prediction with a nugget effect 139
6.4 What does kriging actually do to the data? 140
6.4.1 The prediction weights 141
6.4.2 Varying the correlation parameter 144
6.4.3 Varying the noise to signal ratio 146
xii Contents
6.5 Trans Gaussian kriging 147
6.5.1 Analysis of Swiss rainfall data (continued) 149
6.6 Kriging with non constant mean 151
6.6.1 Analysis of soil calcium data (continued) 151
6.7 Computation 151
6.8 Exercises 155
7 Bayesian inference 157
7.1 The Bayesian paradigm: a unified treatment of estimation and
prediction 157
7.1.1 Prediction using plug in estimates 157
7.1.2 Bayesian prediction 158
7.1.3 Obstacles to practical Bayesian prediction 160
7.2 Bayesian estimation and prediction for the Gaussian linear
model 160
7.2.1 Estimation 161
7.2.2 Prediction when correlation parameters are known . 163
7.2.3 Uncertainty in the correlation parameters 164
7.2.4 Prediction of targets which depend on both the signal
and the spatial trend 165
7.3 Trans Gaussian models 166
7.4 Case studies 167
7.4.1 Surface elevations 167
7.4.2 Analysis of Swiss rainfall data (continued) 169
7.5 Bayesian estimation and prediction for generalized linear
geostatistical models 172
7.5.1 Markov chain Monte Carlo 172
7.5.2 Estimation 173
7.5.3 Prediction 176
7.5.4 Some possible improvements to the MCMC algorithm 177
7.6 Case studies in generalized linear geostatistical modelling . . 179
7.6.1 Simulated data 179
7.6.2 Rongelap island 181
7.6.3 Childhood malaria in The Gambia 185
7.6.4 Loa loa prevalence in equatorial Africa 187
7.7 Computation 193
7.7.1 Gaussian models 193
7.7.2 Non Gaussian models 196
7.8 Exercises 196
8 Geostatistical design 199
8.1 Choosing the study region 201
8.2 Choosing the sample locations: uniform designs 202
8.3 Designing for efficient prediction 203
8.4 Designing for efficient parameter estimation 204
8.5 A Bayesian design criterion 206
8.5.1 Retrospective design 206
Contents xiii
8.5.2 Prospective design 209
8.6 Exercises 211
A Statistical background 213
A.I Statistical models 213
A.2 Classical inference 213
A.3 Bayesian inference 215
A.4 Prediction 216
References 218
Index 227 |
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| author | Diggle, Peter 1950- Ribeiro, Paulo J. |
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| dewey-ones | 550 - Earth sciences |
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| discipline | Geowissenschaften Geologie / Paläontologie Mathematik Geographie |
| discipline_str_mv | Geowissenschaften Geologie / Paläontologie Mathematik Geographie |
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| id | DE-604.BV021783689 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:42:20Z |
| indexdate | 2024-07-09T20:44:00Z |
| institution | BVB |
| isbn | 0387329072 9780387329079 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014996433 |
| oclc_num | 71284654 |
| open_access_boolean | |
| owner | DE-703 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-20 DE-91 DE-BY-TUM DE-521 DE-188 DE-11 |
| owner_facet | DE-703 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-20 DE-91 DE-BY-TUM DE-521 DE-188 DE-11 |
| physical | XIII, 228 S. Ill., graph. Darst., Kt. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Diggle, Peter 1950- Verfasser (DE-588)134228014 aut Model-based geostatistics Peter J. Diggle ; Paulo J. Ribeiro Jr. Model based geostatistics New York [u.a.] Springer 2007 XIII, 228 S. Ill., graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics This volume is the first book-length treatment of model-based geostatistics. The text is expository, emphasizing statistical methods and applications rather than the underlying mathematical theory. Analyses of datasets from a range of scientific contexts feature prominently, and simulations are used to illustrate theoretical results. Readers can reproduce most of the computational results in the book by using the authors' software package, geoR, whose usage is illustrated in a computation section at the end of each chapter. The book assumes a working knowledge of classical and Bayesian methods of inference, linear models, and generalized linear models. Statistics cabt Mathematical Models cabt Geography cabt Geografie Geologie Mathematisches Modell Statistik Geology Mathematical models Geology Statistical methods Geostatistik (DE-588)4020279-3 gnd rswk-swf Geostatistik (DE-588)4020279-3 s DE-604 Ribeiro, Paulo J. Verfasser aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2803937&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014996433&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Diggle, Peter 1950- Ribeiro, Paulo J. Model-based geostatistics Statistics cabt Mathematical Models cabt Geography cabt Geografie Geologie Mathematisches Modell Statistik Geology Mathematical models Geology Statistical methods Geostatistik (DE-588)4020279-3 gnd |
| subject_GND | (DE-588)4020279-3 |
| title | Model-based geostatistics |
| title_alt | Model based geostatistics |
| title_auth | Model-based geostatistics |
| title_exact_search | Model-based geostatistics |
| title_exact_search_txtP | Model-based geostatistics |
| title_full | Model-based geostatistics Peter J. Diggle ; Paulo J. Ribeiro Jr. |
| title_fullStr | Model-based geostatistics Peter J. Diggle ; Paulo J. Ribeiro Jr. |
| title_full_unstemmed | Model-based geostatistics Peter J. Diggle ; Paulo J. Ribeiro Jr. |
| title_short | Model-based geostatistics |
| title_sort | model based geostatistics |
| topic | Statistics cabt Mathematical Models cabt Geography cabt Geografie Geologie Mathematisches Modell Statistik Geology Mathematical models Geology Statistical methods Geostatistik (DE-588)4020279-3 gnd |
| topic_facet | Statistics Mathematical Models Geography Geografie Geologie Mathematisches Modell Statistik Geology Mathematical models Geology Statistical methods Geostatistik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2803937&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014996433&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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