Title: A sparse Gaussian scale mixture process for short-range tail dependence and long-range independence
Authors: Arnab Hazra - King Abdullah University of Science and Technology (Saudi Arabia)
Raphael Huser - King Abdullah University of Science and Technology (Saudi Arabia) [presenting]
Abstract: Various natural phenomena, such as precipitation, exhibit short-range spatial tail dependence. However, the available models in the spatial extremes literature generally assume that spatial tail dependence persists across the entire spatial domain. We develop a novel Bayesian Gaussian scale mixture model, where the Gaussian process component is driven by a stochastic partial differential equation that yields a sparse precision matrix, and the random scale component is modeled as a low-rank Pareto-tailed or Weibull-tailed spatial process determined by compactly supported basis functions. We show that our model is tail-stationary, and we demonstrate that it can capture a wide range of tail dependence structures as a function of distance, such as strong tail dependence at short distances and tail independence at large distances. The sparse structure of our spatial model allows fast Bayesian computation, even in high spatial dimensions. Our inference approach relies on a well-designed Markov chain Monte Carlo algorithm. In our application, we fit our model to analyze heavy monsoon rainfall data in Bangladesh. Numerical experiments show that our model provides a good fit to the data. It can be exploited to draw inferences on long-term return levels for marginal rainfall at each site, and for spatial aggregates.