Comparative Analysis of Spatial Extremes Models and Scalable Inference for Large Spatial Datasets

Music City Center 

Understanding spatial variation in extreme events is crucial for risk management, early warning systems, and policy-making. Spatial extreme datasets exhibit complex dependencies across geographic regions. Examples include maximum temperatures and wind speeds that increase the risk of wildfires, peak river discharges that lead to floods, and low soil moisture affecting crop yields,. While recent advances in spatial extreme models provide more realistic representations of joint tail dependencies, statistical inference remains computationally demanding, especially for large datasets over hundreds of locations. These challenges stem from costly matrix operations on precision matrices and numerical integration in marginal distributions. In this study, we investigate scalable alternatives to full likelihood inference, leveraging advances in spatial modeling, amortized learning, and density regression techniques. We evaluate these methods through simulation studies and apply them to a high-resolution surface skin temperature dataset from the North American Land Data Assimilation System. Our findings provide insights into efficient, data-driven approaches for modeling spatial extremes, paving the way for more practical applications in climate science, environmental risk assessment, and beyond.