| Preface | p. v |
| Contributors | p. xiii |
| An Introduction to MCMC | p. 1 |
| MCMC and spatial statistics | p. 1 |
| The Gibbs sampler | p. 2 |
| The Gibbs sampler and Bayesian statistics | p. 3 |
| Data augmentation | p. 4 |
| Gibbs sampling and convergence | p. 4 |
| The Metropolis-Hastings algorithm | p. 5 |
| Examples of Metropolis-Hastings algorithms | p. 6 |
| The Gibbs sampler | p. 8 |
| MCMC Theory | p. 10 |
| Markov chains and MCMC | p. 10 |
| Convergence in distribution | p. 12 |
| Central limit theorems | p. 13 |
| Practical implementation | p. 14 |
| Sampling from full conditional densities | p. 14 |
| More flexible MCMC algorithms | p. 14 |
| Implementation and output analysis | p. 17 |
| Uses of MCMC in classical statistics and beyond | p. 20 |
| Software | p. 21 |
| An illustrative example | p. 22 |
| Metropolis within Gibbs | p. 22 |
| A collapsed algorithm | p. 23 |
| The independence sampler | p. 24 |
| The multiplicative random walk algorithm | p. 28 |
| Appendix: Model determination using MCMC | p. 29 |
| Introduction | p. 30 |
| Marginal likelihood calculations | p. 31 |
| MCMC model search selection methods | p. 33 |
| References | p. 36 |
| An Introduction to Model-Based Geostatistics | p. 43 |
| Introduction | p. 43 |
| Examples of geostatistical problems | p. 44 |
| Swiss rainfall data | p. 44 |
| Residual contamination of Rongelap Island | p. 44 |
| The general geostatistical model | p. 45 |
| The Gaussian Model | p. 47 |
| Prediction Under The Gaussian Model | p. 50 |
| Extending the Gaussian model | p. 54 |
| Parametric estimation of covariance structure | p. 56 |
| Variogram analysis | p. 56 |
| Maximum likelihood estimation | p. 59 |
| Plug-in prediction | p. 61 |
| The Gaussian model | p. 61 |
| The transformed Gaussian model | p. 61 |
| Non-linear targets | p. 62 |
| Bayesian inference for the linear Gaussian model | p. 63 |
| Fixed correlation parameters | p. 63 |
| Uncertainty in the correlation parameters | p. 64 |
| A Case Study: the Swiss rainfall data | p. 66 |
| Generalised linear spatial models | p. 71 |
| Prediction in a GLSM | p. 72 |
| Bayesian inference for a GLSM | p. 73 |
| A spatial model for count data | p. 75 |
| Spatial model for binomial data | p. 76 |
| Example | p. 77 |
| Discussion | p. 79 |
| Software | p. 81 |
| Further reading | p. 81 |
| References | p. 82 |
| A Tutorial on Image Analysis | p. 87 |
| Introduction | p. 87 |
| Aims of image analysis | p. 87 |
| Bayesian approach | p. 88 |
| Further reading | p. 89 |
| Markov random field models | p. 90 |
| Models for binary and categorical images | p. 92 |
| Models for binary images | p. 92 |
| Models for categorical images | p. 94 |
| Noisy images and the posterior distribution | p. 95 |
| Simulation from the Ising model | p. 96 |
| Simulation from the posterior | p. 101 |
| Image estimators and the treatment of parameters | p. 104 |
| Image functionals | p. 104 |
| Image estimation | p. 104 |
| Inference for nuisance parameters | p. 109 |
| Grey-level images | p. 117 |
| Prior models | p. 118 |
| Likelihood models | p. 120 |
| Example | p. 121 |
| High-level imaging | p. 124 |
| Polygonal models | p. 124 |
| Simulation | p. 126 |
| Marked point process priors | p. 127 |
| Parameter estimation | p. 129 |
| An example in ultrasound imaging | p. 131 |
| Ultrasound imaging | p. 131 |
| Image restoration | p. 133 |
| Contour estimation | p. 136 |
| References | p. 139 |
| An Introduction to Simulation-Based Inference for Spatial Point Processes | p. 143 |
| Introduction | p. 143 |
| Illustrating examples | p. 144 |
| Example 1: Weed plants | p. 144 |
| Example 2: Norwegian spruces | p. 144 |
| What is a spatial point process? | p. 144 |
| Simple point processes in <$>{\op R}^d<$> | p. 146 |
| Marked point processes in <$>{\op R}^d<$> | p. 147 |
| General setting and notation | p. 147 |
| Poisson point processes | p. 148 |
| Definitions and properties | p. 149 |
| Poisson processes in <$>{\op R}^d<$> | p. 150 |
| Marked Poisson processes in <$>{\op R}^d<$> | p. 151 |
| Summary statistics | p. 151 |
| First order characteristics | p. 152 |
| Second order characteristics | p. 152 |
| Nearest-neighbour and empty space functions | p. 156 |
| Example 2: Norwegian spruces (continued) | p. 157 |
| Example 1: Weed plants (continued) | p. 157 |
| Models and simulation-based inference for aggregated point patterns | p. 160 |
| Cox and cluster processes | p. 161 |
| Log Gaussian Cox processes | p. 163 |
| Example 1: Weed plants (continued) | p. 168 |
| Other specific models for Cox processes | p. 170 |
| Models and simulation-based inference for Markov point processes | p. 171 |
| Definitions and properties | p. 172 |
| Pseudo likelihood | p. 174 |
| Example 2: Norwegian spruces (continued) | p. 177 |
| Likelihood inference | p. 177 |
| Example 2: Norwegian spruces (continued) | p. 180 |
| Bayesian inference | p. 183 |
| Metropolis-Hastings algorithms | p. 183 |
| Simulations based on spatial birth-death processes | p. 185 |
| Perfect simulation | p. 186 |
| Further reading and concluding remarks | p. 188 |
| References | p. 190 |
| Index | p. 199 |
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