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Bayesian Regression Modeling with INLA
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Table of Contents

1.Introduction
Quick Start
Hubble's Law
Standard Analysis
Bayesian Analysis
INLA
Bayes Theory
Prior and Posterior Distributions
Model Checking
Model Selection
Hypothesis testing
Bayesian Computation
Exact
Sampling
Approximation

2.Theory of INLA
Latent Gaussian Models (LGMs)
Gaussian Markov Random Fields (GMRFs)
Laplace Approximation and INLA
INLA Problems
Extensions

3.Bayesian Linear Regression
Introduction
Bayesian Inference for Linear Regression
Prediction
Model Selection and Checking
Model Selection by DIC
Posterior Predictive Model Checking
Cross-validation Model Checking
Bayesian Residual Analysis
Robust Regression
Analysis of Variance
Ridge Regression for Multicollinearity
Regression with Autoregressive Errors

4.Generalized Linear Models
GLMs
Binary Responses
Count Responses
Poisson Regression
Negative binomial regression
Modeling Rates
Gamma Regression for Skewed Data
Proportional Responses
Modeling Zero-inflated Data

5.Linear Mixed and Generalized Linear Mixed Models
Linear Mixed Models
Single Random Effect
Choice of Priors
Random Effects
Longitudinal Data
Random Intercept
Random Slope and Intercept
Prediction
Classical Z-matrix Model
Ridge Regression Revisited
Generalized Linear Mixed Models
Poisson GLMM
Binary GLMM
Improving the Approximation

6.Survival Analysis
Introduction
Semiparametric Models
Piecewise Constant Baseline Hazard Models
Stratified Proportional Hazards Models
Accelerated Failure Time Models
Model Diagnosis
Interval Censored Data
Frailty Models
Joint Modeling of Longitudinal and Time-to-event Data

7.Random Walk Models for Smoothing Methods
Introduction
Smoothing Splines
Random Walk (RW) Priors for Equally-spaced Locations
Choice of Priors on s e and sf
Random Walk Models for Non-equally Spaced Locations
Thin-plate Splines
Thin-plate Splines on Regular Lattices
Thin-plate Splines at Irregularly-spaced Locations
Besag Spatial Model
Penalized Regression Splines (P-splines)
Adaptive Spline Smoothing
Generalized Nonparametric Regression Models
Excursion Set with Uncertainty

8.Gaussian Process Regression
Introduction
Penalized Complexity Priors
Credible Bands for Smoothness
Non-stationary Fields
Interpolation with Uncertainty
Survival Response

9.Additive and Generalized Additive Models
Additive Models
Generalized Additive Models
Binary response
Count response
Generalized Additive Mixed Models

10.Errors-in-Variables Regression
Introduction
Classical Errors-in-Variables Models
A simple linear model with heteroscedastic errors-invariables
A general exposure model with replicated measurements
Berkson Errors-in-Variables Models

11.Miscellaneous Topics in INLA
Splines as a Mixed Model
Truncated Power Basis Splines
O'Sullivan Splines
Example: Canadian Income Data
Analysis of Variance for Functional Data
Extreme Values
Density Estimation using INLA

Appendix A Installation
Appendix B Uninformative Priors in Linear Regression
Index

About the Author

Xiaofeng Wang is Professor of Medicine and Biostatistics at the Cleveland Clinic Lerner College of Medicine of Case Western Reserve University and a Full Staff in the Department of Quantitative Health Sciences at Cleveland Clinic. Yu Ryan Yue is Associate Professor of Statistics in the Paul H. Chook Department of Information Systems and Statistics at Baruch College, The City University of New York. Julian J. Faraway is Professor of Statistics in the Department of Mathematical Sciences at the University of Bath.

Reviews

"The book focuses on regression models with R-INLA and it will be of interest to a wide audience. INLA is becoming a very popular method for approximate Bayesian inference and it is being applied to many problems in many different fields. This book will be of interest not only to statisticians but also to applied researchers in other disciplines interested in Bayesian inference. This book can probably be used as a reference book for research and as a textbook at graduate level."
~Virgilio Gomez-Rubio, University of Castilla-La Mancha "This is a well-written book on an important subject, for which there is a lack of good introductory material. The tutorial-style works nicely, and they have an excellent set of examples. They manage to do a practical introduction with just the right amount of theory background...The book should be very useful to scientists who want to analyze data using regression models. INLA allows users to fit Bayesian models quickly and without too much programming effort, and it has been used successfully in many applications. The book is written in a tutorial style, while explaining the basics of the needed theory very well, so it could serve both as a reference or textbook...The book is well written and technically correct."
~Egil Ferkingstad, deCode genetics "The authors have done a great job of not over-doing the technical details, thereby making the presentation accessible to a broader audience beyond the statistics world...It covers many contemporary parametric, nonparametric, and semiparametric methods that applied scientists from many fields use in modern research."
~Adam Branscum, Oregon State University

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