| 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. |