The statistical modeling of spatial extreme events, augmented by graphical models, provides a comprehensive framework for the development of techniques and models to describe natural phenomena in a variety of environmental, geoscience, and climate science applications. In a changing climate, the impact of natural hazards, such as wildfires, is believed to have evolved in frequency, size, and spatial extent, although regional responses may vary. The aforementioned impacts are of great significance due to their association with air pollution, irreversible harm to the environment and atmosphere, and the fact that they put human lives at risk. The prediction of wildfires holds significant importance within the realm of wildfire management due to its influence on the allocation of resources, the mitigation of detrimental consequences, and the subsequent recovery endeavors. Therefore, the development of robust statistical methodologies that can accurately forecast extreme wildfire occurrences across spatial and temporal dimensions is of great significance. In this thesis, we develop new spatial statistical models, combined with popular machine learning techniques, as well as novel extreme-value methods to enhance the prediction of wildfire risk using graphical models. First, in order to jointly efficiently model high-dimensional wildfire counts and burnt areas over the whole continguous United States, we propose a four-stage zero-inflated bivariate spatiotemporal model combining low-rank spatial models and random forests. Second, to model high values of the McArthur Forest Fire Danger Index over Australia, we develop a novel spatial extreme-value model based on mixtures of tree-based multivariate Pareto distributions. Our new methodology combines theoretically justified spatial extreme models with a computationally convenient graphical model framework to spatial problems in high dimensions efficiently. Third, we exploit recent advancements in deep learning and build a parametric regression model using graphic convolutional neural networks and the extended Generalized Pareto distribution, allow us to jointly model moderate and extreme wildfires observed on irregular spatial grid. We work with a novel dataset of Australian wildfires from 1999 to 2019, and analyse monthly spread over areas correspond to Statistical Area Level 1 regions. We highlight the efficacy of our newly proposed model and perform risk assessment for Australia and dense communities.

Saudi Arabia has been trying to change its long tradition of relying on fossil fuels and seek renewable energy sources such as wind power. In this thesis, I firstly provide a comprehensive assessment of wind energy resources and associated spatio-temporal patterns over Saudi Arabia in both current and future climate conditions, based on a Regional Climate Model output. A high wind energy potential exists and is likely to persist at least until 2050 over a vast area ofWestern Saudi Arabia, particularly in the region between Medina and the Red Sea coast and during Summer months. Since an accurate assessment of wind extremes is crucial for risk management purposes, I then present the first high-resolution risk assessment of wind extremes over Saudi Arabia. Under the Bayesian framework, I measure the uncertainty of return levels and produce risk maps of wind extremes, which show that locations in the South of Saudi Arabia and near the Red Sea and the Persian Gulf are at very high risk of disruption of wind turbine operations. In order to perform spatial predictions of the bivariate wind random field for efficient turbine control, I propose parametric variogram matrix (function) models for cokriging, which have the advantage of allowing for a smooth transition between a joint second-order and intrinsically stationary vector random field. Under Gaussianity, the covariance function is central to spatio-temporal modeling, which is useful to understand the dynamics of winds in space and time. I review the various space-time covariance structures and models, some of which are visualized with animations, and associated tests. I also discuss inference issues and a case study based on a high-resolution wind-speed dataset. The Gaussian assumption commonly made in statistics needs to be validated, and I show that tests for independently and identically distributed data cannot be used directly for spatial data. I then propose a new multivariate test for spatial data by accounting for the spatial dependence. The new test is easy to compute, has a chi-square null distribution, and has a good control of the type I error and a high empirical power.

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