Extending INLA to a class of near-Gaussian latent models

This work extends the Integrated Nested Laplace Approximation (INLA) method to latent models outside the scope of latent Gaussian models, where independent components of the latent field can have a near-Gaussian distribution. Two important class of models that can be addressed with our proposed method are non-Gaussian random effects models and dynamic models with non-Gaussian error term for the observation and/or system equation. Our approach is applied to two examples and the results are compared with that obtained by Markov Chain Monte Carlo (MCMC), showing similar accuracy with only a small fraction of computational time. Implementation of the proposed extension is available in the R package INLA.