Hierarchical modeling for extreme values observed over space and time |
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Authors: | Huiyan Sang Alan E Gelfand |
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Institution: | (1) Institute of Statistics and Decision Sciences, Durham, NC, USA |
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Abstract: | We propose a hierarchical modeling approach for explaining a collection of spatially referenced time series of extreme values.
We assume that the observations follow generalized extreme value (GEV) distributions whose locations and scales are jointly
spatially dependent where the dependence is captured using multivariate Markov random field models specified through coregionalization.
In addition, there is temporal dependence in the locations. There are various ways to provide appropriate specifications;
we consider four choices. The models can be fitted using a Markov Chain Monte Carlo (MCMC) algorithm to enable inference for
parameters and to provide spatio–temporal predictions. We fit the models to a set of gridded interpolated precipitation data
collected over a 50-year period for the Cape Floristic Region in South Africa, summarizing results for what appears to be
the best choice of model.
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Keywords: | Coregionalization Generalized extreme value distribution Markov random field Precipitation surfaces Spatial random effects |
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