Spatio-temporal hierarchical Bayesian analysis of wildfires with Stochastic Partial Differential Equations. A case study from Valencian Community (Spain)

The spatio-temporal study of wildfires has two complex elements that are the computational efficiency and longtime processing. Modelling the spatial variability of a wildfire could be performed in different ways, and an important issue is the computational facilities that the new methodological techniques afford us. The Markov random fields methods have made possible to build risk maps, but for many forest managers, it is more advantageous to know the size of the fire and its location. In the first part of this work, Stochastic Partial Differential Equation with Integrated Nested Laplace Approximation is utilised to model the size of the forest fires observed in the Valencian Community (Spain) and so it does the inclusion of the time effect, and the study of the emergency calls. The most crucial element in this paper is the inclusion of the improved meshes for the spatial effect and the time, these are, 2d (locations) and 1d (time) respectively. The advantage of the use of spatio-temporal meshes is described with the inclusion of Bayesian methodology in all the scenarios.