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.


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

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 from the publishers Routledge