Spatial modeling for risk assessment of extreme values from environmental time series: a Bayesian nonparametric approach

We propose an approach to modeling and risk assessment for extremes of environmental processes evolving over time and recorded at a number of spatial locations. We follow an extension of the point process approach to analysis of extremes under which the times of exceedances over a given threshold are assumed to arise from a non-homogeneous Poisson process. To achieve flexible shapes and temporal heterogeneity for the intensity of extremes at any particular spatial location, we utilize a logit-normal mixture model for the corresponding Poisson process density. A spatial Dirichlet process prior for the mixing distributions completes the nonparametric spatio-temporal model formulation. We discuss methods for posterior simulation, using Markov chain Monte Carlo techniques, and develop inference for spatial interpolation of risk assessment quantities for high-level exceedances of the environmental process. The methodology is tested with a synthetic data example and is further illustrated with analysis of rainfall exceedances recorded over a period of 50 years from a region in South Africa. Copyright © 2012 John Wiley & Sons, Ltd.

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