UCSC-SOE-12-17: Spatial modeling for risk assessment of extreme values from environmental time series: A Bayesian nonparametric approach

Athanasios Kottas, Ziwei Wang and Abel Rodriguez
09/29/2012 01:29 PM
Applied Mathematics & Statistics
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.