Fitting dynamic models using integrated nested Laplace approximations - INLA

In this paper we propose a computational framework to perform approximate Bayesian inference in linear and generalized linear dynamic models based on the Integrated Nested Laplace Approximation (INLA) approach, which overcomes some limitations of computational tools presently available in the dynamic modeling literature. We show how to formulate specific latent models in a state-space form, even for more complex cases, such as growth models and spatio-temporal dynamic models, in order to perform approximate inference on them using the INLA library, a user-friendly interface for using INLA with the R programming language. A first approach uses existing model options in the INLA library and is suitable to model first order random walk evolution and seasonal behavior of simpler dynamic models. A generic approach is also proposed to formulate and fit dynamic models in a more general setting, which is useful with more complex models, such as spatio-temporal dynamic models. The combination of the two approaches is also possible. The proposed framework is illustrated with a series of simulated as well as worked real-life examples. This computational framework for inference enables the fitting of several kinds of dynamic models, including realistically complex spatio-temporal models, in an easy way and in a short computational time.