Incluye bibliografía e índice: páginas 305-308

Preface.. 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.. 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.. 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.. 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.. 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.. 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.. 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.. 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

The Bayesian approach is particularly effective at modeling large datasets including spatial and temporal information due to its flexibility and ease with which it can formally include correlation and hierarchical structures in the data. However, classical simulation methods such as Markov Chain Monte Carlo can become computationally unfeasible; this book presents the Integrated Nested Laplace Approximations (INLA) approach as a computationally effective and extremely powerful alternative. Spatial and Spatio-temporal Bayesian Models with R-INLA introduces the basic paradigms of the Bayesian approach and describes the associated computational issues. Detailing the theory behind the INLA approach and the R-INLA package, it focuses on spatial and spatio-temporal modeling for area and point-referenced data. The combination of detailed theory and practical data analysis is beneficial for readers at any level. The coding of all the examples in R-INLA and the availability of all the datasets used throughout the book on the INLA website (www.r-inla.org) make an appealing feature for applied researchers wanting to approach or increase their knowledge and practice of the INLA method. Inglés