Case studies in Bayesian computation using INLA

Abstract

Latent Gaussian models are a common construct in statistical applications where a latent Gaussian field, indirectly observed through data, is used to model, for instance, time and space dependence or the smooth effect of covariates. Many well-known statistical models, such as smoothing-spline models, space time models, semiparametric regression, spatial and spatio-temporal models, log-Gaussian Cox models, and geostatistical models are latent Gaussian models. Integrated Nested Laplace approximation (INLA) is a new approach to implement Bayesian inference for such models. It provides approximations of the posterior marginals of the latent variables which are both very accurate and extremely fast to compute. Moreover, INLA treats latent Gaussian models in a general way, thus allowing for a great deal of automation in the inferential procedure. The inla programme, bundled in the R library INLA, is a prototype of such black-box for inference on latent Gaussian models which is both flexible and user-friendly. It is meant to, hopefully,make latent Gaussian models applicable, useful and appealing for a larger class of users.