Spatial Data Analysis withR-INLAwith Some Extensions

The integrated nested Laplace approximation (INLA) provides an interesting way ofapproximating the posterior marginals of a wide range of Bayesian hierarchical models.This approximation is based on conducting a Laplace approximation of certain functionsand numerical integration is extensively used to integrate some of the models parametersout.TheR-INLApackage o ers an interface to INLA, providing a suitable framework fordata analysis. Although the INLA methodology can deal with a large number of models,only the most relevant have been implemented withinR-INLA. However, many otherimportant models are not available forR-INLAyet.In this paper we show how to fit a number of spatial models withR-INLA, including itsinteraction with otherRpackages for data analysis. Secondly, we describe a novel methodto extend the number of latent models available for the model parameters. Our approachis based on conditioning on one or several model parameters and fit these conditionedmodels with R-INLA. Then these models are combined using Bayesian model averagingto provide the final approximations to the posterior marginals of the model.Finally, we show some examples of the application of this technique in spatial statistics.It is worth noting that our approach can be extended to a number of other fields, and notonly spatial statistic