1st Edition

Bayesian inference with INLA

By Virgilio Gomez-Rubio Copyright 2020
    332 Pages
    by Chapman & Hall

    330 Pages
    by Chapman & Hall

    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.

    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  


    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