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.
Table of Contents
- Introduction to Bayesian Inference
- The Integrated Nested Laplace Approximation
- Mixed-effects Models
- Multilevel Models
- Priors in R-INLA
- Advanced Features
- Spatial Models
- Temporal Models
- Survival Models
- Implementing New Latent Models
- Missing Values and Imputation
Markov chain Monte Carlo
The integrated nested Laplace approximation
An introductory example: U’s in Game of Thrones books
The Integrated Nested Laplace Approximation
The R-INLA package
Model assessment and model choice
Working with posterior marginals
Sampling from the posterior
Types of mixed-effects models
Information on the latent effects
Multilevel models with random effects
Multilevel models with nested effects
Multilevel models with complex structure
Multilevel models for longitudinal data
Multilevel models for binary data
Multilevel models for count data
Selection of priors
Implementing new priors
Penalized Complexity priors
Sensitivity analysis with R-INLA
Scaling effects and priors
Smooth terms with INLA
Smoothing with SPDE
Non-parametric estimation of the survival curve
Parametric modeling of the survival function
Semi-parametric estimation: Cox proportional hazards
Accelerated failure time models
Spatial latent effects
R implementation with rgeneric
Bayesian model averaging
INLA within MCMC
Comparison of results
Missing values in the response
Imputation of missing covariates
Multiple imputation of missing values
13. Mixture models
Bayesian analysis of mixture models
Fitting mixture models with INLA
Model selection for mixture models
Cure rate models
Packages used in the book
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).
"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-INLA…The 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-INLA…It 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 solved…Overall the book is like a tutorial with several examples in several different areas of statistical modeling…This 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