INLA stands for Integrated Nested Laplace Approximations, which is a new method for fitting a broad class of Bayesian regression models. No samples of the posterior marginal distributions need to be drawn using INLA, so it is a computationally convenient alternative to Markov chain Monte Carlo (MCMC), the standard tool for Bayesian inference.

Bayesian Regression Modeling with INLA covers a wide range of modern regression models and focuses on the INLA technique for building Bayesian models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to demonstrate the interplay of theory and practice with reproducible studies. Complete R commands are provided for each example, and a supporting website holds all of the data described in the book. An R package including the data and additional functions in the book is available to download.

The book is aimed at readers who have a basic knowledge of statistical theory and Bayesian methodology. It gets readers up to date on the latest in Bayesian inference using INLA and prepares them for sophisticated, real-world work.

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.

chapter 1|18 pages


chapter 2|20 pages

Theory of INLA

chapter 3|31 pages

Bayesian Linear Regression

chapter 4|29 pages

Generalized Linear Models

chapter 6|28 pages

Survival analysis

chapter 7|42 pages

Random Walk Models for Smoothing Methods

chapter 8|17 pages

Gaussian Process Regression

chapter 9|21 pages

Additive and Generalized Additive Models

chapter 10|16 pages

Errors-in-Variables Regression

chapter 11|21 pages

Miscellaneous Topics in INLA