Bayesian inference with INLA: 1st Edition (Hardback) book cover

Bayesian inference with INLA

1st Edition

By Virgilio Gomez-Rubio

Chapman and Hall/CRC

337 pages

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Hardback: 9781138039872
pub: 2020-04-01
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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, social sciences and other.

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

    Geostatistics

    Point patterns

  15. Temporal Models
  16. Introduction

    Autoregressive models

    Non-Gaussian data

    Forecasting

    Space-state models

    Spatio-temporal models

    Final remarks

  17. Smoothing
  18. Introduction

    Splines

    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

Introduction

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

About the Author

Virgilio Gómez-Rubio is associate professor in the Department of Mathematics, 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.

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
MED090000
MEDICAL / Biostatistics