Spatial Models Using Laplace Approximation Methods

Bayesian inference has been at the center of the development of spatial statistics in recent years. In particular, Bayesian hierarchical models including several fixed and random effects have become very popular in many different fields. Given that inference on these models is seldom available in closed form, model fitting is usually based on simulation methods such as Markov chain Monte Carlo. However, these methods are often very computationally expensive and a number of approximations have been developed. The integrated nested Laplace approximation (INLA) provides a general approach to computing the posterior marginals of the parameters in the model. INLA focuses on latent Gaussian models, but this is a class of methods wide enough to tackle a large number of problems in spatial statistics. In this chapter, we describe the main advantages of the integrated nested Laplace approximation. Applications to many different problems in spatial statistics will be discussed as well.