The impact of choosing different meshes under INLA/SPDE framework for geostatistical modelling - Righetto, Ana Julia (2017)
Spatial statistics methods are widely used since several areas of knowledge such as environmental sciences, geology, agronomy, among others, involve the understanding of the spatial distribution of processes from spatially referenced data. With the advancement of Geographic Information Systems and the Global Positioning Systems this use has been extended. Many methods used in spatial statistics are computationally demanding, and therefore, the development of more computationally efficient methods has received a lot of attention in recent years. One such important development is the introduction of the integrated nested Laplace approximation method which is able to carry out Bayesian analysis in a more efficient way. The use of this method for geostatistical data is commonly done considering the stochastic partial differential equation approach that requires the creation of a mesh overlying the study area. This is the first and an important step since all results will depend on the choice of this mesh. As there is no formal and close way to specify the mesh, we investigate possible guidelines on how a suitable mesh is chosen for a specific problem. Through simulations studies, we tried to create guidelines for the construction of the mesh for random, regular and cluster data set and we aplly this guidelines in real data set.