In a previous blog post I described the construction of Confidence Bands for Smoothness. The idea is to express the uncertainty in the amount of smoothing to be applied when fitting functions to data using Gaussian process regression. Now you can do the same thing with INLA. The previous implementation is in STAN. This is quite fast but not as fast as INLA.
I am writing a book entitled Bayesian Regression with INLA with Xiaofeng Wang and Ryan Yue. INLA stands for integrated nested Laplace approximations. Bayesian computation is not straightforward. In a few simple cases, explicit solutions exist, but in most statistical applications one typically uses simulation – usually based on MCMC (Markov chain Monte Carlo) methods. In some cases, this simulation can take a long time so it would be nice if you could do it faster. INLA is an approximation-based method that can do some Bayesian model fitting computation very quickly compared to simulation-based methods. You can learn more at the R-INLA website. You can also see some preview examples from the book.