Likun Zhang - Colloquium Speaker
Extreme events over large spatial domains like the contiguous United States may exhibit highly heterogeneous tail dependence characteristics, yet most existing spatial extremes models yield only one dependence class over the entire spatial domain. To accurately characterize ‘storm dependence’ in analysis of extreme events, we propose a mixture model that achieves flexible dependence properties and allows truly high-dimensional inference for extremes of spatial processes. We modify the popular random scale construction that multiplies a Gaussian random field by a single radial variable; that is, we add non-stationarity to the Gaussian process while allowing the radial variable to vary smoothly across space. As the level of extremeness increases, this single model exhibits both long-range asymptotic independence and short-range weakening dependence strength that can lead to either asymptotic dependence or independence. Under the assumption of local stationarity, we make inference on the model parameters using local Bayesian hierarchical models and run adaptive Metropolis algorithms concurrently via parallelization. Then, after conducting posterior inference locally, the mixture component representation of the model coherently ties the local posteriors together to obtain a globally nonstationary model.