Spatial and Spatio-Temporal Bayesian Models with R-INLA provides a much needed, practically oriented & innovative presentation of the combination of Bayesian methodology and spatial statistics. The authors combine an introduction to Bayesian theory and methodology with a focus on the spatial and spatio -temporal models used within the Bayesian framework and a series of practical examples which allow the reader to link the statistical theory presented to real data problems. The numerous examples from the fields of epidemiology, biostatistics and social science all are coded in the R package R-INLA, which has proven to be a valid alternative to the commonly used Markov Chain Monte Carlo simulations

Spatial and Spatio-Temporal Bayesian Models withR-INLA provides a much needed, practically oriented& innovative presentation of the combination of Bayesianmethodology and spatial statistics. The authors combine anintroduction to Bayesian theory and methodology with a focus on thespatial and spatio--temporal models used within the Bayesianframework and a series of practical examples which allow the readerto link the statistical theory presented to real data problems. Thenumerous examples from the fields of epidemiology, biostatisticsand social science all are coded in the R package R-INLA, which hasproven to be a valid alternative to the commonly used Markov ChainMonte Carlo simulations

Dedication iiiPreface ix1 Introduction 11.1 Why spatial and spatio-temporal statistics? 11.2 Why do we use Bayesian methods for modelling spatial and spatio-temporal structures? 21.3 Why INLA? 31.4 Datasets 32 Introduction to 212.1 The language 212.2 objects 222.3 Data and session management 342.4 Packages 352.5 Programming in 362.6 Basic statistical analysis with 393 Introduction to Bayesian Methods 533.1 Bayesian Philosophy 533.2 Basic Probability Elements 573.3 Bayes Theorem 623.4 Prior and Posterior Distributions 643.5 Working with the Posterior Distribution 663.6 Choosing the Prior Distribution 684 Bayesian computing 834.1 Monte Carlo integration 834.2 Monte Carlo method for Bayesian inference 854.3 Probability distributions and random number generation in 864.4 Examples of Monte Carlo simulation 894.5 Markov chain Monte Carlo methods 974.6 The Integrated Nested Laplace Approximations algorithm 1134.7 Laplace approximation 1134.8 The package 1234.9 How INLA works: step by step example 1275 Bayesian regression and hierarchical models 1395.1 Linear Regression 1395.2 Nonlinear regression: random walk 1455.3 Generalized Linear Models 1505.4 Hierarchical Models 1595.5 Prediction 1765.6 Model Checking and Selection 1796 Spatial Modeling 1896.1 Areal data -GMRF 1926.2 Ecological Regression 2036.3 Zero inated models 2046.4 Geostatistical data 2106.5 The Stochastic Partial Diferential Equation approach 2116.6 SPDE within 2156.7 SPDE toy example with simulated data 2176.8 More advanced operations through the function 2266.9 Prior specification for the stationary case 2336.10 SPDE for Gaussian response: Swiss rainfall data 2376.11 SPDE with nonnormal outcome: Malaria in the Gambia 2456.12 Prior specification for the nonstationary case 2497 Spatio-Temporal Models 2577.1 Spatio-temporal Disease mapping 2587.2 Spatio-temporal Modeling particulate matter concentration 2688 Advanced modeling 2838.1 Bivariate model for spatially misaligned data 2838.2 Semicontinuous model to daily rainfall 2958.3 Spatio-temporal dynamic models 3088.4 Space-time model lowering the time resolution 321