Marta Blangiardo, Michela Cameletti

Spatial and Spatio-temporal Bayesian Models with R - INLA (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 320
• Erscheinungstermin: 7. April 2015
• Englisch
• ISBN-13: 9781118950197
• Artikelnr.: 42643486

Autorenporträt

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

Inhaltsangabe

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