Model-Based Geostatistics for Global Public Health: Methods and Applications
In: Chapman and Hall/CRC Interdisciplinary Statistics Ser.
Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- List of Figures -- List of Tables -- 1: Introduction -- 1.1 Motivating example: mapping river-blindness in Africa -- 1.2 Empirical or mechanistic models -- 1.3 What is in this book? -- 2: Regression modelling for spatially referenced data -- 2.1 Linear regression models -- 2.1.1 Malnutrition in Ghana -- 2.2 Generalised linear models -- 2.2.1 Logistic Binomial regression: river-blindness in Liberia -- 2.2.2 Log-linear Poisson regression: abundance of Anopheles Gambiae mosquitoes in Southern Cameroon -- 2.3 Questioning the assumption of independence -- 2.3.1 Testing for residual spatial correlation: the empirical variogram -- 3: Theory -- 3.1 Gaussian processes -- 3.2 Families of spatial correlation functions -- 3.2.1 The exponential family -- 3.2.2 The Matérn family -- 3.2.3 The spherical family -- 3.2.4 The theoretical variogram and the nugget variance -- 3.3 Statistical inference -- 3.3.1 Likelihood-based inference -- 3.4 Bayesian Inference -- 3.5 Predictive inference -- 3.6 Approximations to Gaussian processes -- 3.6.1 Low-rank approximations -- 3.6.2 Gaussian Markov random field approximations via stochastic partial differential equations -- 4: The linear geostatistical model -- 4.1 Model formulation -- 4.2 Inference -- 4.2.1 Likelihood-based inference -- 4.2.1.1 Maximum likelihood estimation -- 4.2.2 Bayesian inference -- 4.2.3 Trans-Gaussian models -- 4.3 Model validation -- 4.3.1 Scenario 1: omission of the nugget effect -- 4.3.2 Scenario 2: miss-specification of the smoothness parameter -- 4.3.3 Scenario 3: non-Gaussian data -- 4.4 Spatial prediction -- 4.5 Applications -- 4.5.1 Heavy metal monitoring in Galicia -- 4.5.2 Malnutrition in Ghana (continued) -- 4.5.2.1 Spatial predictions for the target population.