Fitting complex Bayesian models with R-INLA and MCMC
The Integrated Nested Laplace Approximation (INLA) provides a computationally efficient approach to obtaining an approximation to the posterior marginals for a large number of Bayesian models. In particular, INLA focuses on those models that can be expressed as a Latent Gaussian Markov Random field. Its associated R package, R-INLA, implements a number of functions to easily fit many of these models. However, it is not easy to implement new latent models or priors. Bivand et al. (2014) proposed a way of using R-INLA to fit models that are not implemented, by fixing some parameters in the model and then combining the fitted models using Bayesian Model Averaging (BMA). This is implemented in the INLABMA R package. An interesting feature of this approach is that it allows Bayesian models to be fitted in parallel. Recently, Gomez-Rubio et al. (2016) have proposed the use of MCMC and INLA together to fit more complex models. This approach allows INLA to fit models with unimplemented (or multivariate) priors, missing data in the covariates and many more latent models. Finally, we will explore how these ideas can be applied to fit models to Big Data. This involves fitting models to separate chunks of data with R-INLA and then combining the output to obtain an approximation to the model with all the data.
References: Bivand et al. (2014). Approximate Bayesian Inference for Spatial Econometrics Models. Spatial Statistics 9, 146-165.
Gomez-Rubio et al. (2016). Extending INLA with MCMC. Work in progress.