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.

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

I am the author of a forthcoming book entitled Bayesian Regression Models with Xiaofeng Wang and Ryan Yue

You will need to install the brinla R package to run many of the examples described here.

- Introduction - a simple example concerning Hubbleâ€™s law.
- Linear regression - Chicago Insurance data
- One-way ANOVA - just one random effect
- Ridge regression - Ridge regression with meat spectroscopy data
- Gaussian Process regression - GP regression on fossil data
- Confidence bands for smoothness - GP regression to determine uncertainty regarding smoothness
- Non-stationary smoothing - GP regression with variable smoothing
- Generalized Extreme Values - fitting maximum annual river flows
- Define your own prior - using a half Cauchy prior for the SD of a random effect.

See also linear mixed models examples from my Extending Linear Models with R book.