Enhancing the SPDE modeling of spatial point processes with INLA, applied to wildfires. Choosing the best mesh for each database

Wildfires play an important role in shaping landscapes and as a source of CO2 and particulate matter, and are a typical spatial point process studied in many papers. Modeling the spatial variability of a wildfire could be performed in different ways and an important issue is the computational facilities that the new techniques afford us. The most common approaches have been through point pattern analysis or by Markov random fields. These methods have made it possible to build risk maps, but for many forest managers it is very useful to know the size of the fire as well as its location. In this work, we use Stochastic Partial Differential Equation (SPDE) with Integrated Nested Laplace Approximation (INLA) to model the size of the forest fires observed in the Valencian Community, Spain. But the most important element in this paper is the process that needs to be carried out prior to simulating and analyzing the different point patterns, namely, the choice of the most suitable mesh for the database. We describe and take advantage of the Bayesian methodology by including INLA and SPDE in the modeling process in all the scenarios.

Automated summary

Wildfires play a significant role in shaping landscapes and as a source of CO2 and particulate matter, and are often studied as a typical spatial point process. Various methods, such as point pattern analysis or Markov random fields, can be used to model the spatial variability of wildfires. In this study, the size of forest fires in the Valencian Community, Spain was modeled using Stochastic Partial Differential Equation (SPDE) with Integrated Nested Laplace Approximation (INLA).