A combined statistical and machine learning approach for spatial prediction of extreme wildfire frequencies and sizes

Motivated by the Extreme Value Analysis 2021 (EVA 2021) data challenge we propose a method based on statistics and machine learning for the spatial prediction of extreme wildfire frequencies and sizes. This method is tailored to handle large datasets, including missing observations. Our approach relies on a four-stage high-dimensional bivariate sparse spatial model for zero-inflated data, which is developed using stochastic partial differential equations(SPDE). In Stage 1, the observations are categorized in zero/nonzero categories and are modeled using a two-layered hierarchical Bayesian sparse spatial model to estimate the probabilities of these two categories. In Stage 2, before modeling the positive observations using spatially-varying coefficients, smoothed parameter surfaces are obtained from empirical estimates using fixed rank kriging. This approximate Bayesian method inference was employed to avoid the high computational burden of large spatial data modeling using spatially-varying coefficients. In Stage 3, the standardized log-transformed positive observations from the second stage are further modeled using a sparse bivariate spatial Gaussian process. The Gaussian distribution assumption for wildfire counts developed in the third stage is computationally effective but erroneous. Thus in Stage 4, the predicted values are rectified using Random Forests. The posterior inference is drawn for Stages 1 and 3 using Markov chain Monte Carlo (MCMC) sampling. A cross-validation scheme is then created for the artificially generated gaps, and the EVA 2021 prediction scores of the proposed model are compared to those obtained using certain natural competitors.