Bayesian Regression with INLA

A book by Xiaofeng Wang, Ryan Yue and Julian Faraway

INLA stands for Integrated Nested Laplace Approximations. It is used for fitting Latent Gaussian models (LGM). LGMs include a wide range of commonly used regression models. Unlike MCMC which uses simulation methods, INLA uses approximation methods for Bayesian model fitting. Within the class of LGMs, INLA can fit models much faster than MCMC-based methods.

Chapter scripts

  1. Introduction: intro.R with output
  2. Theory of INLA: inla.R
  3. Linear Regression: blr.R
  4. Generalized Linear Models: glm.R
  5. Generalized Linear Mixed Models glmm.R with output
  6. Survival Analysis: surv.R
  7. Random Walk Models for Smoothing: npr.R
  8. Gaussian Process Regression gpr.R with output
  9. Generalized Additive Models: gam.R
  10. Errors-in-Variables Regression: eiv.R
  11. Miscellaneous Topics: misc.R

R package

The brinla R package contains data and functions to support the book.

Visit the INLA website to learn much more including how to install the INLA R package.

Install the brinla package with:



Here are the errata. If you find any other errata, please let us know according to the chapter: Ch3, 4, 6, 10 (Xiaofeng Wang), Ch2, 7 or 9 (Ryan Yue) or Ch1, 5 or 8 (Julian Faraway).


Here are some examples


The book can be purchased at the usual online outlets or the publishers