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Name: Arnab Hazra

Talk Title: A sparse Gaussian scale mixture process for modeling short-range extremal dependence and long-range independence

Abstract: Various natural phenomena, such as precipitation, generally exhibit extremal dependence at short distances only, while spatial dependence usually fades away as the distance between sites increases arbitrarily. However, the available methods in the literature for spatial extremes, which are based on max-stable or Pareto processes or comparatively less computationally demanding “sub-asymptotic” models based on location and/or scale mixtures, generally assume that spatial extremal dependence persists across the entire spatial domain. In this paper, we develop a novel Bayesian Gaussian scale mixture model, where the Gaussian process component is driven through a stochastic partial differential equation (SPDE) 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 extremal dependence structures as a function of distance. The sparse structure of our spatial model allows fast Bayesian computations, even in high spatial dimensions. In our application, we fit our model to analyze heavy monsoon rainfall data in Bangladesh. Our inference approach relies on a well-designed Markov chain Monte Carlo (MCMC) algorithm. A cross-validation study indicates that the proposed model outperforms some natural alternatives, and that the model provides a good fit to the rainfall data. Finally, we use the fitted model to draw inferences on long-term return levels for marginal rainfall at each site, and for spatial aggregates.

This talk is a contributed talk at EVA 2021.