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

Abstract

Wildfires play an important role in shaping landscapes and as a source of CO 2 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.

Modeling Influence of Soil Properties in Different Gradients of Soil Moisture: The Case of the Valencia Anchor Station Validation Site, Spain

“…To tackle this task, the Integrated Nested Laplace Approximation (INLA) [25,26] approach was applied to identify the variables that affect moisture. The advantage of using INLA over other methods, such as basic statistical methods, or other more complex methods, such as Markov Change Monte Carlo (MCMC) or Generalized Linear Models (GLM), is that INLA works in reasonable computational times by allowing the user to quickly and efficiently work with complex models [25,28,29] allows as many covariates as desired to be integrated, and even incorporate new ones into the model in later steps and it does not require any work being conducted exclusively with normal distributions as it is based on Bayesian inference.…”

“…The actual meteorological station that gives the name to the site was been installed (N 39.570740 [25,26]. These methodologies have been highly developed and applied, e.g., [27][28][29] and constitute one step ahead of the classical Geostatistics with kriging. The rest of the paper is organized as follows.…”

“…R software [40] and the Bayesian estimation methodology, including the basic features of INLA approach and the SPDE [25,26], were used to fit parametric models to the observed spatial patterns, including covariates that will play the role of risk factors showing spatial variability of the data, as it is feasible with this approach [28]. A technical difficulty to fit models using continuously indexed Gaussian random fields is the big n problem, which imposes restrictions on the size of the matrices that have to be inverted in the model fitting process.…”

“…We use Stochastic Partial Differential Equation (SPDE) with Integrated Nested Laplace Approximation (INLA) [25,26]. These methodologies have been highly developed and applied, e.g., [27][28][29] and constitute one step ahead of the classical Geostatistics with kriging.…”