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
- Introduction to Bayesian Inference
- The Integrated Nested Laplace Approximation
- Mixed-effects Models
- Multilevel Models
- Priors in R-INLA
- Advanced Features
- Spatial Models
- Temporal Models
- Smoothing
- Survival Models
- Implementing New Latent Models
- Missing Values and Imputation
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
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
Introduction
Fixed-effects models
Types of mixed-effects models
Information on the latent effects
Additional arguments
Final remarks
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
Introduction
Selection of priors
Implementing new priors
Penalized Complexity priors
Sensitivity analysis with R-INLA
Scaling effects and priors
Final remarks
Introduction
Predictor Matrix
Linear combinations
Several likelihoods
Shared terms
Linear constraints
Final remarks
Introduction
Areal data
Geostatistics
Point patterns
Introduction
Autoregressive models
Non-Gaussian data
Forecasting
Space-state models
Spatio-temporal models
Final remarks
Introduction
Splines
Smooth terms with INLA
Smoothing with SPDE
Non-Gaussian models
Final remarks
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
Introduction
Spatial latent effects
R implementation with rgeneric
Bayesian model averaging
INLA within MCMC
Comparison of results
Final remarks
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
