Title: Spatial Models with the Integrated Nested Laplace Approximation within Markov Chain Monte Carlo,
Abstract: The Integrated Nested Laplace Approximation (INLA) is a convenient way to
obtain approximations to the posterior marginals for parameters in Bayesian
hierarchical models when the latent effects can be expressed as a Gaussian
Markov Random Field (GMRF). In addition, its implementation in the R-INLA
package for the R statistical software provides an easy way to fit models using
INLA in practice. R-INLA implements a number of widely used latent models,
including several spatial models. In addition, R-INLA can fit models in a
fraction of the time than other computer intensive methods (e.g. Markov Chain
Monte Carlo) take to fit the same model.
Although INLA provides a fast approximation to the marginals of the model
parameters, it is difficult to use it with models not implemented in R-INLA. It
is also difficult to make multivariate posterior inference on the parameters of
the model as INLA focuses on the posterior marginals and not the joint
posterior distribution.
In this paper we describe how to use INLA within the Metropolis-Hastings
algorithm to fit spatial models and estimate the joint posterior distribution
of a reduced number of parameters. We will illustrate the benefits of this new
method with two examples on spatial econometrics and disease mapping where
complex spatial models with several spatial structures need to be fitted.