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248 Pages
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orGeostatistics is concerned with estimation and prediction problems for spatially continuous phenomena, using data obtained at a limited number of spatial locations. The name reflects its origins in mineral exploration, but the methods are now used in a wide range of settings including public health and the physical and environmental sciences. Model-based geostatistics refers to the application of general statistical principles of modeling and inference to geostatistical problems. This volume is the first book-length treatment of model-based geostatistics.
The authors have written an expository text, 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' R-based 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, but does not require previous exposure to spatial statistical models or methods. The authors have used the material in MSc-level statistics courses.
Industry Reviews
| Preface | p. v |
| Introduction | p. 1 |
| Motivating examples | p. 1 |
| Terminology and notation | p. 9 |
| Support | p. 9 |
| Multivariate responses and explanatory variables | p. 10 |
| Sampling design | p. 12 |
| Scientific objectives | p. 12 |
| Generalised linear geostatistical models | p. 13 |
| What is in this book? | p. 15 |
| Organisation of the book | p. 16 |
| Statistical pre-requisites | p. 17 |
| Computation | p. 17 |
| Elevation data | p. 17 |
| More on the geodata object | p. 20 |
| Rongelap data | p. 22 |
| The Gambia malaria data | p. 24 |
| The soil data | p. 24 |
| Exercises | p. 26 |
| An overview of model-based geostatistics | p. 27 |
| Design | p. 27 |
| Model formulation | p. 28 |
| Exploratory data analysis | p. 30 |
| Non-spatial exploratory analysis | p. 30 |
| Spatial exploratory analysis | p. 31 |
| The distinction between parameter estimation and spatial prediction | p. 35 |
| Parameter estimation | p. 36 |
| Spatial prediction | p. 37 |
| Definitions of distance | p. 39 |
| Computation | p. 40 |
| Exercises | p. 45 |
| Gaussian models for geostatistical data | p. 46 |
| Covariance functions and the variogram | p. 46 |
| Regularisation | p. 48 |
| Continuity and differentiability of stochastic processes | p. 49 |
| Families of covariance functions and their properties | p. 51 |
| The Matern family | p. 51 |
| The powered exponential family | p. 53 |
| Other families | p. 54 |
| The nugget effect | p. 56 |
| Spatial trends | p. 57 |
| Directional effects | p. 58 |
| Transformed Gaussian models | p. 60 |
| Intrinsic models | p. 63 |
| Unconditional and conditional simulation | p. 66 |
| Low-rank models | p. 68 |
| Multivariate models | p. 69 |
| Cross-covariance, cross-correlation and cross-variogram | p. 70 |
| Bivariate signal and noise | p. 71 |
| Some simple constructions | p. 72 |
| Computation | p. 74 |
| Exercises | p. 77 |
| Generalized linear models for geostatistical data | p. 79 |
| General formulation | p. 79 |
| The approximate covariance function and variogram | p. 81 |
| Examples of generalised linear geostatistical models | p. 82 |
| The Poisson log-linear model | p. 82 |
| The binomial logistic-linear model | p. 83 |
| Spatial survival analysis | p. 84 |
| Point process models and geostatistics | p. 86 |
| Cox processes | p. 87 |
| Preferential sampling | p. 89 |
| Some examples of other model constructions | p. 93 |
| Scan processes | p. 93 |
| Random sets | p. 94 |
| Computation | p. 94 |
| Simulating from the generalised linear model | p. 94 |
| Preferential sampling | p. 96 |
| Exercises | p. 97 |
| Classical parameter estimation | p. 99 |
| Trend estimation | p. 100 |
| Variograms | p. 100 |
| The theoretical variogram | p. 100 |
| The empirical variogram | p. 102 |
| Smoothing the empirical variogram | p. 102 |
| Exploring directional effects | p. 104 |
| The interplay between trend and covariance structure | p. 105 |
| Curve-fitting methods for estimating covariance structure | p. 107 |
| Ordinary least squares | p. 108 |
| Weighted least squares | p. 108 |
| Comments on curve-fitting methods | p. 110 |
| Maximum likelihood estimation | p. 112 |
| General ideas | p. 112 |
| Gaussian models | p. 112 |
| Profile likelihood | p. 114 |
| Application to the surface elevation data | p. 114 |
| Restricted maximum likelihood estimation for the Gaussian linear model | p. 116 |
| Trans-Gaussian models | p. 117 |
| Analysis of Swiss rainfall data | p. 118 |
| Analysis of soil calcium data | p. 121 |
| Parameter estimation for generalized linear geostatistical models | p. 123 |
| Monte Carlo maximum likelihood | p. 124 |
| Hierarchical likelihood | p. 125 |
| Generalized estimating equations | p. 125 |
| Computation | p. 126 |
| Variogram calculations | p. 126 |
| Parameter estimation | p. 130 |
| Exercises | p. 132 |
| Spatial prediction | p. 134 |
| Minimum mean square error prediction | p. 134 |
| Minimum mean square error prediction for the stationary Gaussian model | p. 136 |
| Prediction of the signal at a point | p. 136 |
| Simple and ordinary kriging | p. 137 |
| Prediction of linear targets | p. 138 |
| Prediction of non-linear targets | p. 138 |
| Prediction with a nugget effect | p. 139 |
| What does kriging actually do to the data? | p. 140 |
| The prediction weights | p. 141 |
| Varying the correlation parameter | p. 144 |
| Varying the noise-to-signal ratio | p. 146 |
| Trans-Gaussian kriging | p. 147 |
| Analysis of Swiss rainfall data (continued) | p. 149 |
| Kriging with non-constant mean | p. 151 |
| Analysis of soil calcium data (continued) | p. 151 |
| Computation | p. 151 |
| Exercises | p. 155 |
| Bayesian inference | p. 157 |
| The Bayesian paradigm: a unified treatment of estimation and prediction | p. 157 |
| Prediction using plug-in estimates | p. 157 |
| Bayesian prediction | p. 158 |
| Obstacles to practical Bayesian prediction | p. 160 |
| Bayesian estimation and prediction for the Gaussian linear model | p. 160 |
| Estimation | p. 161 |
| Prediction when correlation parameters are known | p. 163 |
| Uncertainty in the correlation parameters | p. 164 |
| Prediction of targets which depend on both the signal and the spatial trend | p. 165 |
| Trans-Gaussian models | p. 166 |
| Case studies | p. 167 |
| Surface elevations | p. 167 |
| Analysis of Swiss rainfall data (continued) | p. 169 |
| Bayesian estimation and prediction for generalized linear geostatistical models | p. 172 |
| Markov chain Monte Carlo | p. 172 |
| Estimation | p. 173 |
| Prediction | p. 176 |
| Some possible improvements to the MCMC algorithm | p. 177 |
| Case studies in generalized linear geostatistical modelling | p. 179 |
| Simulated data | p. 179 |
| Rongelap island | p. 181 |
| Childhood malaria in The Gambia | p. 185 |
| Loa loa prevalence in equatorial Africa | p. 187 |
| Computation | p. 193 |
| Gaussian models | p. 193 |
| Non-Gaussian models | p. 196 |
| Exercises | p. 196 |
| Geostatistical design | p. 199 |
| Choosing the study region | p. 201 |
| Choosing the sample locations: uniform designs | p. 202 |
| Designing for efficient prediction | p. 203 |
| Designing for efficient parameter estimation | p. 204 |
| A Bayesian design criterion | p. 206 |
| Retrospective design | p. 206 |
| Prospective design | p. 209 |
| Exercises | p. 211 |
| Statistical background | p. 213 |
| Statistical models | p. 213 |
| Classical inference | p. 213 |
| Bayesian inference | p. 215 |
| Prediction | p. 216 |
| References | p. 218 |
| Index | p. 227 |
| Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780387329079
ISBN-10: 0387329072
Series: Springer Series in Statistics
Published: 1st March 2007
Format: Hardcover
Language: English
Number of Pages: 248
Audience: College, Tertiary and University
Publisher: Springer Nature B.V.
Country of Publication: GB
Dimensions (cm): 31 x 18 x 2
Weight (kg): 0.52
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