  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.
