Approximate Bayesia Inference for Latent Gaussian Models

Latent Gaussian models are a common construct in statistical applications where some latent field, which is assumed to have a Gaussian structure, is undirectly observed through conditional independent data. We consider cases where the observational model is non-Gaussian. The class of latent Gaussian models includes many well known statistical models. The latent Gaussian field can, in fact, be used to model, for instance, the time and space dependence among data or the smooth effect of covariates. Hence, smoothing-spline models, space time models, semi-parametric regression, spatial and spatio-temporal models, log-Gaussian Cox models, and geostatistical models, all fall into this category. Integrated Nested Laplace approximation (INLA) is a new approach to Bayesian inference for latent Gaussian model. It provides accurate approximations to the posterior marginals of the latent variables conditioned on the observed data. INLA constitutes a fast, deterministic alternative to MCMC which, at the moment, is the standard tool for inference in such models. The main advantage of INLA over MCMC is that it is much faster to compute. Results are obtained in second and minutes where MCMC would require hours and days. Moreover INLA allows for a great deal of automation and parallelization of all computational procedures, hence different kind of models, for example spatial or spatio-temporal ones, can be treated in exactly the same way. The program ``inla'' , which is now part of the GMRFLib library, and its R interface make the INLA approach easily available for the user and practically no programming at all is needed. Our experience shows that INLA outperforms without comparison any MCMC alternative, both in terms of accuracy and computational speed