Title Page; Copyright; Table of Contents; Dedication; 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; References; 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; References; Chapter 3: Introduction to Bayesian methods; 3.1 Bayesian philosophy; 3.2 Basic probability elements; 3.3 Bayes theorem
3.4 Prior and posterior distributions3.5 Working with the posterior distribution; 3.6 Choosing the prior distribution; References; 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; 4.6 The integrated nested Laplace approximations algorithm; 4.7 Laplace approximation; 4.8 The R-INLA package; 4.9 How INLA works: step-by-step example; References
Chapter 5: Bayesian regression and hierarchical models5.1 Linear regression; 5.2 Nonlinear regression: random walk; 5.3 Generalized linear models; 5.4 Hierarchical models; 5.5 Prediction; 5.6 Model checking and selection; References; Chapter 6: Spatial modeling; 6.1 Areal data -- GMRF; 6.2 Ecological regression; 6.3 Zero-inflated models; 6.4 Geostatistical data; 6.5 The stochastic partial differential equation approach; 6.6 SPDE within R-INLA; 6.7 SPDE toy example with simulated data; 6.8 More advanced operations through the inla.stack function; 6.9 Prior specification for the stationary case
6.10 SPDE for Gaussian response: Swiss rainfall data6.11 SPDE with nonnormal outcome: malaria in the Gambia; 6.12 Prior specification for the nonstationary case; References; Chapter 7: Spatio-temporal models; 7.1 Spatio-temporal disease mapping; 7.2 Spatio-temporal modeling particulate matter concentration; References; Chapter 8: Advanced modeling; 8.1 Bivariate model for spatially misaligned data; 8.2 Semicontinuous model to daily rainfall; 8.3 Spatio-temporal dynamic models; 8.4 Space-time model lowering the time resolution; References; Index; End User License Agreement
Summary
Spatial and Spatio-Temporal Bayesian Models with R-INLA provides a muchneeded, practically oriented & innovative presentation of the combination ofBayesian methodology and spatial statistics. The authors combine an introduction toBayesian theory and methodology with a focus on the spatial and spatio-temporal modelsused within the Bayesian framework and a series of practical examples which allowthe reader to link the statistical theory presented to real data problems. The numerousexamples from the fields of epidemiology, biostatistics and social science all arecoded in the R package R-INLA, which has proven to be a valid alternative to the commonlyused Markov Chain Monte Carlo simulations
Bibliography
Includes bibliographical references and index
Notes
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