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Spatial modeling for risk assessment of extreme values from environmental time series: a Bayesian nonparametric approach
Author(s) -
Kottas Athanasios,
Wang Ziwei,
Rodríguez Abel
Publication year - 2012
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.2177
Subject(s) - markov chain monte carlo , nonparametric statistics , point process , dirichlet process , cox process , spatial dependence , econometrics , bayesian probability , inference , computer science , statistics , poisson distribution , bayesian inference , mathematics , poisson process , artificial intelligence
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.