Estimating the marginal likelihood with Integrated nested Laplace approximation (INLA)

Understand

The marginal likelihood is a well established model selection criterion in Bayesian statistics.

• It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities of interest.
• For many complex models, including latent modeling approaches, marginal likelihoods are however difficult to compute.
• One recent promising approach for approximating the marginal likelihood is Integrated Nested Laplace Approximation (INLA), design for models with latent Gaussian structures.