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E-raamat: Spatial and Spatio-temporal Bayesian Models with R - INLA

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  • Formaat: EPUB+DRM
  • Ilmumisaeg: 07-Apr-2015
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118950197
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Spatial and Spatio-temporal Bayesian Models with R - INLASuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 07-Apr-2015
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118950197
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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
Preface xi
1 Introduction
1(18)
1.1 Why spatial and spatio-temporal statistics?
1(1)
1.2 Why do we use Bayesian methods for modeling spatial and spatio-temporal structures?
2(1)
1.3 Why INLA?
3(1)
1.4 Datasets
3(16)
1.4.1 National Morbidity, Mortality, and Air Pollution Study
4(1)
1.4.2 Average income in Swedish municipalities
4(1)
1.4.3 Stroke in Sheffield
5(1)
1.4.4 Ship accidents
6(1)
1.4.5 CD4 in HIV patients
6(1)
1.4.6 Lip cancer in Scotland
7(1)
1.4.7 Suicides in London
8(1)
1.4.8 Brain cancer in Navarra, Spain
9(1)
1.4.9 Respiratory hospital admission in Turin province
10(1)
1.4.10 Malaria in the Gambia
11(1)
1.4.11 Swiss rainfall data
11(2)
1.4.12 Lung cancer mortality in Ohio
13(1)
1.4.13 Low birth weight births in Georgia
14(1)
1.4.14 Air pollution in Piemonte
14(5)
2 Introduction to R
19(28)
2.1 The R language
19(1)
2.2 R objects
20(11)
2.3 Data and session management
31(1)
2.4 Packages
32(1)
2.5 Programming in R
33(2)
2.6 Basic statistical analysis with R
35(12)
3 Introduction to Bayesian methods
47(28)
3.1 Bayesian philosophy
47(4)
3.1.1 Thomas Bayes and Simon Pierre Laplace
47(2)
3.1.2 Bruno de Finetti and colleagues
49(1)
3.1.3 After the Second World War
49(1)
3.1.4 The 1990s and beyond
50(1)
3.2 Basic probability elements
51(5)
3.2.1 What is an event?
51(1)
3.2.2 Probability of events
51(3)
3.2.3 Conditional probability
54(2)
3.3 Bayes theorem
56(1)
3.4 Prior and posterior distributions
57(3)
3.4.1 Bayesian inference
58(2)
3.5 Working with the posterior distribution
60(1)
3.6 Choosing the prior distribution
61(14)
3.6.1 Type of distribution
62(5)
3.6.2 Conjugacy
67(1)
3.6.3 Noninformative or informative prior
67(8)
4 Bayesian computing
75(52)
4.1 Monte Carlo integration
75(2)
4.2 Monte Carlo method for Bayesian inference
77(1)
4.3 Probability distributions and random number generation in R
78(2)
4.4 Examples of Monte Carlo simulation
80(9)
4.5 Markov chain Monte Carlo methods
89(15)
4.5.1 Gibbs sampler
91(6)
4.5.2 Metropolis---Hastings algorithm
97(6)
4.5.3 MCMC implementation: software and output analysis
103(1)
4.6 The integrated nested Laplace approximations algorithm
104(1)
4.7 Laplace approximation
105(7)
4.7.1 INLA setting: the class of latent Gaussian models
107(2)
4.7.2 Approximate Bayesian inference with INLA
109(3)
4.8 The R-INLA package
112(6)
4.9 How INLA works: step-by-step example
118(9)
5 Bayesian regression and hierarchical models
127(46)
5.1 Linear regression
128(4)
5.1.1 Comparing the Bayesian to the classical regression model
128(2)
5.1.2 Example: studying the relationship between temperature and PM10
130(2)
5.2 Nonlinear regression: random walk
132(6)
5.2.1 Example: studying the relationship between average household age and income in Sweden
136(2)
5.3 Generalized linear models
138(7)
5.4 Hierarchical models
145(17)
5.4.1 Exchangeability
148(2)
5.4.2 INLA as a hierarchical model
150(1)
5.4.3 Hierarchical regression
151(3)
5.4.4 Example: a hierarchical model for studying CD4 counts in AIDS patients
154(2)
5.4.5 Example: a hierarchical model for studying lip cancer in Scotland
156(5)
5.4.6 Example: studying stroke mortality in Sheffield (UK)
161(1)
5.5 Prediction
162(3)
5.6 Model checking and selection
165(8)
5.6.1 Methods based on the predictive distribution
166(3)
5.6.2 Methods based on the deviance
169(4)
6 Spatial modeling
173(62)
6.1 Areal data --- GMRF
176(10)
6.1.1 Disease mapping
177(2)
6.1.2 BYM model: suicides in London
179(7)
6.2 Ecological regression
186(2)
6.3 Zero-inflated models
188(5)
6.3.1 Zero-inflated Poisson model: brain cancer in Navarra
188(2)
6.3.2 Zero-inflated binomial model: air pollution and respiratory hospital admissions
190(3)
6.4 Geostatistical data
193(1)
6.5 The stochastic partial differential equation approach
194(4)
6.5.1 Nonstationary Gaussian field
197(1)
6.6 SPDE within R-INLA
198(1)
6.7 SPDE toy example with simulated data
199(9)
6.7.1 Mesh construction
200(4)
6.7.2 The observation or projector matrix
204(2)
6.7.3 Model fitting
206(2)
6.8 More advanced operations through the inla. stack function
208(6)
6.8.1 Spatial prediction
210(4)
6.9 Prior specification for the stationary case
214(3)
6.9.1 Example with simulated data
215(2)
6.10 SPDE for Gaussian response: Swiss rainfall data
217(8)
6.11 SPDE with nonnormal outcome: malaria in the Gambia
225(4)
6.12 Prior specification for the nonstationary case
229(6)
6.12.1 Example with simulated data
229(6)
7 Spatio-temporal models
235(24)
7.1 Spatio-temporal disease mapping
236(10)
7.1.1 Nonparametric dynamic trend
238(2)
7.1.2 Space---time interactions
240(6)
7.2 Spatio-temporal modeling particulate matter concentration
246(13)
7.2.1 Change of support
253(6)
8 Advanced modeling
259(46)
Elias T. Krainski
8.1 Bivariate model for spatially misaligned data
259(11)
8.1.1 Joint model with Gaussian distributions
261(6)
8.1.2 Joint model with non-Gaussian distributions
267(3)
8.2 Semicontinuous model to daily rainfall
270(13)
8.3 Spatio-temporal dynamic models
283(12)
8.3.1 Dynamic model with Besag proper specification
284(3)
8.3.2 Dynamic model with genericl specification
287(8)
8.4 Space---time model lowering the time resolution
295(10)
8.4.1 Spatio-temporal model
300(5)
Index 305
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
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