Dr. Likun Zhang - Two paths to Scalable Nonstationary Tail Dependence: A Scale-Aware Bayesian Model and an XVAE Alternative

Spatial extremes remain difficult to model. Yet many widely used spatial extremes models impose a single dependence regime across an entire domain, which can distort risk assessment. I will present two recent papers that target the same challenges: (1) building flexible, scale-aware tail dependence that accommodates realistic nonstationarity, and (2) achieving computational scalability to hundreds-to-thousands of spatial locations. The first approach develops a Bayesian hierarchical model that extends random-scale constructions by allowing the strength and class of tail dependence to vary across space, while also incorporating nonstationary latent spatial structure. The resulting model can capture long-range asymptotic independence while permitting either local asymptotic dependence or independence. Inference is carried out with carefully engineered MCMC that leverages extensive parallelization and optimized numerical routines to make high-dimensional analysis feasible at modern observational scale. The second approach attacks the bottleneck from a deep-learning angle: we propose a VAE-based framework that learns expressive dependence representations and enables ultra-fast approximate inference via gradient-based optimization. I will contrast the modeling assumptions, uncertainty quantification, and computational tradeoffs, and discuss when each paradigm is preferable for scientific goals such as regional risk mapping, spatial prediction, and sensitivity to tail decay.