  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. The
proposed methodology is an essential component of a bigger project that aim to
extend the R package INLA (R-INLA) in order to allow the user to add
flexibility and challenge the Gaussian assumptions of some of the model
components in a straightforward and intuitive way. 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-INLA package.
