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E-grāmata: Bayesian inference with INLA

(Universidad de Castilla-La Mancha, Albacete, Spain)
  • Formāts: 330 pages
  • Izdošanas datums: 20-Feb-2020
  • Izdevniecība: CRC Press
  • ISBN-13: 9781351707190
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Bayesian inference with INLAPalielināt
  • Formāts: 330 pages
  • Izdošanas datums: 20-Feb-2020
  • Izdevniecība: CRC Press
  • ISBN-13: 9781351707190
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The integrated nested Laplace approximation (INLA) is a recent computational method that can fit Bayesian models in a fraction of the time required by typical Markov chain Monte Carlo (MCMC) methods. INLA focuses on marginal inference on the model parameters of latent Gaussian Markov random fields models and exploits conditional independence properties in the model for computational speed.

Bayesian Inference with INLA

provides a description of INLA and its associated R package for model fitting. This book describes the underlying methodology as well as how to fit a wide range of models with R. Topics covered include generalized linear mixed-effects models, multilevel models, spatial and spatio-temporal models, smoothing methods, survival analysis, imputation of missing values, and mixture models. Advanced features of the INLA package and how to extend the number of priors and latent models available in the package are discussed. All examples in the book are fully reproducible and datasets and R code are available from the book website.

This book will be helpful to researchers from different areas with some background in Bayesian inference that want to apply the INLA method in their work. The examples cover topics on biostatistics, econometrics, education, environmental science, epidemiology, public health, and the social sciences.

Recenzijas

"I strongly recommend the book `Bayesian inference with INLA and R-INLA written by Virgilio Gomez-Rubio for anyone working in analysing data using R-INLA. The book is well-written and focuses not only on variety models with INLA and R-INLA but also on how to extend the usage of R-INLA. It has a nice and well-planned layout. The practical tutorial-style works nicely and it has an excellent set of examples. The author manages to cover a large amount of technical details; therefore the book will be interest to a wide audience such as students, statisticians and applied researchers. The book has all the details for both basic and advanced knowledge on using INLA and R-INLAThe book could serve both as a reference for researchers or textbook for both introductory and advanced class." ~Jingyi Guo Fuglstad, Norwegian University of Science and Technology

"The book is technically correct and clearly written. The level of difficulty is appropriate for practitioners or those interested in knowing the possibilities of R-INLAIt stands as a first read for people interested in using R-INLA to fit latent Gaussian models-based models. It will be more of a reference book. One can learn how to solve a problem by reading one of the examples and then solve a similar problem. One can also get inspired with the idea in an example and do a bit more complex model from this. The tricks explored in some examples may be useful to solve diverse other problems, like the copy feature." ~Gianluca Baio, University College London

"The book under review is well-written, has a clear and logical structure, and provides a comprehensive overview of models that can be fitted with R-INLA. The author consistently provides the R code embedded within the text, which is a crucial feature, especially for those who want to replicate the coding procedure for similar case studies using their own data." ~Andre Python, University of Oxford

"The book adopts a brief style in most of the chapters. In each example, it gives a general idea of the problem and jumps directly to showing how to solve it. The details are not explored in the examples but only what is need for getting the problem solvedOverall the book is like a tutorial with several examples in several different areas of statistical modelingThis book will be a good reference book for introducing INLA in a Bayesian applied course. This will be also useful for researches who intend to apply INLA when modeling with the class of models for which INLA is suitable. It can be the first source of inspiration for those who need to solve a problem similar to one of those considered in the book." ~Elias T. Krainski, Universidade Federal do Para

Preface xi
1 Introduction to Bayesian Inference
1(12)
1.1 Introduction
1(1)
1.2 Bayesian inference
1(1)
1.3 Conjugate priors
2(1)
1.4 Computational methods
3(1)
1.5 Markov chain Monte Carlo
3(1)
1.6 The integrated nested Laplace approximation
4(1)
1.7 An introductory example: U's in Game of Thrones books
5(6)
1.8 Final remarks
11(2)
2 The Integrated Nested Laplace Approximation
13(26)
2.1 Introduction
13(1)
2.2 The Integrated Nested Laplace Approximation
13(4)
2.3 The R-INLA package
17(7)
2.4 Model assessment and model choice
24(4)
2.5 Control options
28(2)
2.6 Working with posterior marginals
30(5)
2.7 Sampling from the posterior
35(4)
3 Mixed-effects Models
39(36)
3.1 Introduction
39(1)
3.2 Fixed-effects models
39(3)
3.3 Types of mixed-effects models
42(21)
3.4 Information on the latent effects
63(1)
3.5 Additional arguments
63(10)
3.6 Final remarks
73(2)
4 Multilevel Models
75(28)
4.1 Introduction
75(1)
4.2 Multilevel models with random effects
75(7)
4.3 Multilevel models with nested effects
82(5)
4.4 Multilevel models with complex structure
87(3)
4.5 Multilevel models for longitudinal data
90(3)
4.6 Multilevel models for binary data
93(4)
4.7 Multilevel models for count data
97(6)
5 Priors in R-INLA
103(16)
5.1 Introduction
103(1)
5.2 Selection of priors
103(4)
5.3 Implementing new priors
107(4)
5.4 Penalized Complexity priors
111(2)
5.5 Sensitivity analysis with R-INLA
113(1)
5.6 Scaling effects and priors
114(2)
5.7 Final remarks
116(3)
6 Advanced Features
119(22)
6.1 Introduction
119(1)
6.2 Predictor Matrix
119(2)
6.3 Linear combinations
121(7)
6.4 Several likelihoods
128(3)
6.5 Shared terms
131(7)
6.6 Linear constraints
138(2)
6.7 Final remarks
140(1)
7 Spatial Models
141(36)
7.1 Introduction
141(1)
7.2 Areal data
141(14)
7.3 Geostatistics
155(11)
7.4 Point patterns
166(11)
8 Temporal Models
177(24)
8.1 Introduction
177(1)
8.2 Autoregressive models
177(6)
8.3 Non-Gaussian data
183(4)
8.4 Forecasting
187(1)
8.5 Space-state models
188(4)
8.6 Spatio-temporal models
192(6)
8.7 Final remarks
198(3)
9 Smoothing
201(18)
9.1 Introduction
201(1)
9.2 Splines
201(5)
9.3 Smooth terms with INLA
206(6)
9.4 Smoothing with SPDE
212(2)
9.5 Non-Gaussian models
214(4)
9.6 Final remarks
218(1)
10 Survival Models
219(24)
10.1 Introduction
219(1)
10.2 Non-parametric estimation of the survival curve
220(2)
10.3 Parametric modeling of the survival function
222(2)
10.4 Semi-parametric estimation: Cox proportional hazards
224(3)
10.5 Accelerated failure time models
227(3)
10.6 Frailty models
230(3)
10.7 Joint modeling
233(10)
11 Implementing New Latent Models
243(16)
11.1 Introduction
243(1)
11.2 Spatial latent effects
243(2)
11.3 R implementation with rgeneric
245(6)
11.4 Bayesian model averaging
251(3)
11.5 INLA within MCMC
254(3)
11.6 Comparison of results
257(1)
11.7 Final remarks
257(2)
12 Missing Values and Imputation
259(20)
12.1 Introduction
259(1)
12.2 Missingness mechanism
259(1)
12.3 Missing values in the response
260(7)
12.4 Imputation of missing covariates
267(5)
12.5 Multiple imputation of missing values
272(5)
12.6 Final remarks
277(2)
13 Mixture models
279(20)
13.1 Introduction
279(1)
13.2 Bayesian analysis of mixture models
279(4)
13.3 Fitting mixture models with INLA
283(6)
13.4 Model selection for mixture models
289(4)
13.5 Cure rate models
293(5)
13.6 Final remarks
298(1)
Packages used in the book 299(4)
Bibliography 303(10)
Index 313
Virgilio Gómez-Rubio is associate professor in the Department of Mathematics, School of Industrial Engineering, Universidad de Castilla-La Mancha, Albacete, Spain. He has developed several packages on spatial and Bayesian statistics that are available on CRAN, as well as co-authored books on spatial data analysis and INLA including Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA (CRC Press, 2019).
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