Spatial and Spatio-temporal Bayesian Models with R - INLA

Informationen zum Autor Marta Blangiardo , MRC-PHE Centre for Environment and Health, Department of Epidemiology and Biostatistics, Imperial College London, UK Michela Cameletti , Department of Management, Economics and Quantitative Methods, University of Bergamo, Italy Klappentext 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 Zusammenfassung 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. Inhaltsverzeichnis 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 inflated 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...

Autorentext
Marta Blangiardo, MRC-PHE Centre for Environment and Health, Department of Epidemiology and Biostatistics, Imperial College London, UK Michela Cameletti, Department of Management, Economics and Quantitative Methods, University of Bergamo, Italy

Klappentext
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

Inhalt
Dedication iii Preface ix 1 Introduction 1 1.1 Why spatial and spatio-temporal statistics? 1 1.2 Why do we use Bayesian methods for modelling spatial and spatio-temporal structures? 2 1.3 Why INLA? 3 1.4 Datasets 3 2 Introduction to 21 2.1 The language 21 2.2 objects 22 2.3 Data and session management 34 2.4 Packages 35 2.5 Programming in 36 2.6 Basic statistical analysis with 39 3 Introduction to Bayesian Methods 53 3.1 Bayesian Philosophy 53 3.2 Basic Probability Elements 57 3.3 Bayes Theorem 62 3.4 Prior and Posterior Distributions 64 3.5 Working with the Posterior Distribution 66 3.6 Choosing the Prior Distribution 68 4 Bayesian computing 83 4.1 Monte Carlo integration 83 4.2 Monte Carlo method for Bayesian inference 85 4.3 Probability distributions and random number generation in 86 4.4 Examples of Monte Carlo simulation 89 4.5 Markov chain Monte Carlo methods 97 4.6 The Integrated Nested Laplace Approximations algorithm 113 4.7 Laplace approximation 113 4.8 The package 123 4.9 How INLA works: step by step example 127 5 Bayesian regression and hierarchical models 139 5.1 Linear Regression 139 5.2 Nonlinear regression: random walk 145 5.3 Generalized Linear Models 150 5.4 Hierarchical Models 159 5.5 Prediction 176 5.6 Model Checking and Selection 179 6 Spatial Modeling 189 6.1 Areal data -GMRF 192 6.2 Ecological Regression 203 6.3 Zero inflated models 204 6.4 Geostatistical data 210 6.5 The Stochastic Partial Diferential Equation approach 211 6.6 SPDE within 215 6.7 SPDE toy example with simulated data 217 6.8 More advanced operations through the function 226 6.9 Prior specification for the stationary case 233 6.10 SPDE for Gaussian response: Swiss rainfall data 237 6.11 SPDE with nonnormal outcome: Malaria in the Gambia 245 6.12 Prior specification for the nonstationary case 249 7 Spatio-Temporal Models 257 7.1 Spatio-temporal Disease mapping 258 7.2 Spatio-temporal Modeling particulate matter concentration 268 8 Advanced modeling 283 8.1 Bivariate model for spatially misaligned data 283 8.2 Semicontinuous model to daily rainfall 295 8.3 Spatio-temporal dynamic models 308 8.4 Space-time model lowering the time resolution 321

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