The change of support problem through the INLA approach

This paper concerns the change of support problem (COSP) for continuos spatial phenomena which are commonly observed at the point and/or area level. A change of the spatial scale can be required for predicting the process of interest at a resolution which is different from the one at which the data are observed or for fusing data coming from several sources and characterized by different spatial resolutions. COSP may be a computationally demanding task as it involves stochastic integration of the continuos spatial process. For this reason, in case of complex models or huge data, Bayesian inference with Markov chain Monte Carlo (MCMC) may become unfeasible and some modeling simplifications may be required. In this paper we present how to manage the COSP through the Integrated Nested Laplace approximation approach (INLA), which is a computationally effective alternative to MCMC for Bayesian inference, and the Stochastic Partial Differential Equation (SPDE) approach, which gains computational benefits by approximating a continuos spatial process as a Gaussian Markov random field (through a basis function representation). An environmental applications regarding particulate matter pollution shows how to obtain spatial predictions at a new spatial resolution without worsening the computational load.