Bayesian nonparametric regression and density estimation using integrated nested Laplace approximations.

Integrated nested Laplace approximations (INLA) are a recently proposed approximate Bayesian approach to fit structured additive regression models with latent Gaussian field. INLA method, as an alternative to Markov chain Monte Carlo techniques, provides accurate approximations to estimate posterior marginals and avoid time-consuming sampling. We show here that two classical nonparametric smoothing problems, nonparametric regression and density estimation, can be achieved using INLA. Simulated examples and R functions are demonstrated to illustrate the use of the methods. Some discussions on potential applications of INLA are made in the paper.