Bayesian inference with INLA  book cover
1st Edition

Bayesian inference with INLA

ISBN 9781032174532
Published September 30, 2021 by Chapman & Hall
332 Pages

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Book Description

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

  1. Introduction to Bayesian Inference
  2. Introduction

    Bayesian inference

    Conjugate priors

    Computational methods

    Markov chain Monte Carlo

    The integrated nested Laplace approximation

    An introductory example: U’s in Game of Thrones books

    Final remarks

  3. The Integrated Nested Laplace Approximation
  4. Introduction

    The Integrated Nested Laplace Approximation

    The R-INLA package

    Model assessment and model choice

    Control options

    Working with posterior marginals

    Sampling from the posterior

  5. Mixed-effects Models
  6. Introduction

    Fixed-effects models

    Types of mixed-effects models

    Information on the latent effects

    Additional arguments

    Final remarks

  7. Multilevel Models
  8. Introduction

    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

  9. Priors in R-INLA
  10. Introduction

    Selection of priors

    Implementing new priors

    Penalized Complexity priors

    Sensitivity analysis with R-INLA

    Scaling effects and priors

    Final remarks

  11. Advanced Features
  12. Introduction

    Predictor Matrix

    Linear combinations

    Several likelihoods

    Shared terms

    Linear constraints

    Final remarks

  13. Spatial Models
  14. Introduction

    Areal data


    Point patterns

  15. Temporal Models
  16. Introduction

    Autoregressive models

    Non-Gaussian data


    Space-state models

    Spatio-temporal models

    Final remarks

  17. Smoothing
  18. Introduction


    Smooth terms with INLA

    Smoothing with SPDE

    Non-Gaussian models

    Final remarks

  19. Survival Models
  20. Introduction

    Non-parametric estimation of the survival curve

    Parametric modeling of the survival function

    Semi-parametric estimation: Cox proportional hazards

    Accelerated failure time models

    Frailty models

    Joint modeling

  21. Implementing New Latent Models
  22. Introduction

    Spatial latent effects

    R implementation with rgeneric

    Bayesian model averaging

    INLA within MCMC

    Comparison of results

    Final remarks

  23. Missing Values and Imputation
  24. Introduction

    Missingness mechanism

    Missing values in the response

    Imputation of missing covariates

    Multiple imputation of missing values

    Final remarks

13.     Mixture models


          Bayesian analysis of mixture models

          Fitting mixture models with INLA

          Model selection for mixture models

          Cure rate models

          Final remarks

          Packages used in the book  

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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