ABSTRACT
Bayesian inference has relied upon Markov chain Monte Carlo methods to compute the joint posterior distribution of the model parameters. A Gaussian approximation is possible, but Rue et al. obtain better approximations by resorting to other methods, such as the Laplace approximation. Integrated nested Laplace approximation (INLA) computes a number of Bayesian criteria for model assessment and model choice. Model assessment criteria are useful to check whether a given model is doing a good job at representing the data, while model choice criteria will be of help when selecting among different models. In order to compare all these different criteria and see them in action, the models for the sudden infant death syndrome dataset will be refit and these criteria computed. As INLA focuses on the posterior marginal distributions of the latent effects and the hyperparameters it is important to be able to exploit these for inference.
