Cover -- Title Page -- Copyright -- Contents -- Preface -- Chapter 1 Introduction -- 1.1 Why spatial and spatio-temporal statistics? -- 1.2 Why do we use Bayesian methods for modeling spatial and spatio-temporal structures? -- 1.3 Why INLA? -- 1.4 Datasets -- 1.4.1 National Morbidity, Mortality, and Air Pollution Study -- 1.4.2 Average income in Swedish municipalities -- 1.4.3 Stroke in Sheffield -- 1.4.4 Ship accidents -- 1.4.5 CD4 in HIV patients -- 1.4.6 Lip cancer in Scotland -- 1.4.7 Suicides in London -- 1.4.8 Brain cancer in Navarra, Spain -- 1.4.9 Respiratory hospital admission in Turin province -- 1.4.10 Malaria in the Gambia -- 1.4.11 Swiss rainfall data -- 1.4.12 Lung cancer mortality in Ohio -- 1.4.13 Low birth weight births in Georgia -- 1.4.14 Air pollution in Piemonte -- Chapter 2 Introduction to R -- 2.1 The R language -- 2.2 R objects -- 2.3 Data and session management -- 2.4 Packages -- 2.5 Programming in R -- 2.6 Basic statistical analysis with R -- Chapter 3 Introduction to Bayesian methods -- 3.1 Bayesian philosophy -- 3.1.1 Thomas Bayes and Simon Pierre Laplace -- 3.1.2 Bruno de Finetti and colleagues -- 3.1.3 After the Second World War -- 3.1.4 The 1990s and beyond -- 3.2 Basic probability elements -- 3.2.1 What is an event? -- 3.2.2 Probability of events -- 3.2.3 Conditional probability -- 3.3 Bayes theorem -- 3.4 Prior and posterior distributions -- 3.4.1 Bayesian inference -- 3.5 Working with the posterior distribution -- 3.6 Choosing the prior distribution -- 3.6.1 Type of distribution -- 3.6.2 Conjugacy -- 3.6.3 Noninformative or informative prior -- Chapter 4 Bayesian computing -- 4.1 Monte Carlo integration -- 4.2 Monte Carlo method for Bayesian inference -- 4.3 Probability distributions and random number generation in R -- 4.4 Examples of Monte Carlo simulation.

4.5 Markov chain Monte Carlo methods -- 4.5.1 Gibbs sampler -- 4.5.2 Metropolis-Hastings algorithm -- 4.5.3 MCMC implementation: software and output analysis -- 4.6 The integrated nested Laplace approximations algorithm -- 4.7 Laplace approximation -- 4.7.1 INLA setting: the class of latent Gaussian models -- 4.7.2 Approximate Bayesian inference with INLA -- 4.8 The R-INLA package -- 4.9 How INLA works: step-by-step example -- Chapter 5 Bayesian regression and hierarchical models -- 5.1 Linear regression -- 5.1.1 Comparing the Bayesian to the classical regression model -- 5.1.2 Example: studying the relationship between temperature and PM10 -- 5.2 Nonlinear regression: random walk -- 5.2.1 Example: studying the relationship between average household age and income in Sweden -- 5.3 Generalized linear models -- 5.4 Hierarchical models -- 5.4.1 Exchangeability -- 5.4.2 INLA as a hierarchical model -- 5.4.3 Hierarchical regression -- 5.4.4 Example: a hierarchical model for studying CD4 counts in AIDS patients -- 5.4.5 Example: a hierarchical model for studying lip cancer in Scotland -- 5.4.6 Example: studying stroke mortality in Sheffield (UK) -- 5.5 Prediction -- 5.6 Model checking and selection -- 5.6.1 Methods based on the predictive distribution -- 5.6.2 Methods based on the deviance -- Chapter 6 Spatial modeling -- 6.1 Areal data - GMRF -- 6.1.1 Disease mapping -- 6.1.2 BYM model: suicides in London -- 6.2 Ecological regression -- 6.3 Zero-inflated models -- 6.3.1 Zero-inflated Poisson model: brain cancer in Navarra -- 6.3.2 Zero-inflated binomial model: air pollution and respiratory hospital admissions -- 6.4 Geostatistical data -- 6.5 The stochastic partial differential equation approach -- 6.5.1 Nonstationary Gaussian field -- 6.6 SPDE within R-INLA -- 6.7 SPDE toy example with simulated data.

6.7.1 Mesh construction -- 6.7.2 The observation or projector matrix -- 6.7.3 Model fitting -- 6.8 More advanced operations through the inla.stack function -- 6.8.1 Spatial prediction -- 6.9 Prior specification for the stationary case -- 6.9.1 Example with simulated data -- 6.10 SPDE for Gaussian response: Swiss rainfall data -- 6.11 SPDE with nonnormal outcome: malaria in the Gambia -- 6.12 Prior specification for the nonstationary case -- 6.12.1 Example with simulated data -- Chapter 7 Spatio-temporal models -- 7.1 Spatio-temporal disease mapping -- 7.1.1 Nonparametric dynamic trend -- 7.1.2 Space-time interactions -- 7.2 Spatio-temporal modeling particulate matter concentration -- 7.2.1 Change of support -- Chapter 8 Advanced modeling -- 8.1 Bivariate model for spatially misaligned data -- 8.1.1 Joint model with Gaussian distributions -- 8.1.2 Joint model with non-Gaussian distributions -- 8.2 Semicontinuous model to daily rainfall -- 8.3 Spatio-temporal dynamic models -- 8.3.1 Dynamic model with Besag proper specification -- 8.3.2 Dynamic model with generic1 specification -- 8.4 Space-time model lowering the time resolution -- 8.4.1 Spatio-temporal model -- Index -- EULA.