A semiparametric Bayesian model for spatiotemporal extremes
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In this paper, we consider a Dirichlet process mixture of spatial skew-t processes that can flexibly model the extremes as well as the bulk, with separate parameters controlling spatial dependence in these two parts of the distribution. The proposed model has nonstationary mean and covariance structure and also nonzero spatial asymptotic dependence. Max-stable processes are theoretically justified model for station-wise block maximums or threshold exceedances in the spatial extremes literature. Considering a high threshold leads to somewhat arbitrary decision about what counts as extreme, and more importantly, it disallows the possibility that events that are large but deemed insufficiently extreme can enter into the analysis at all. Probabilistic clustering of the extreme observations and allowing extremal dependence for the cluster of extremes is a solution that is explored here. Inference is drawn based on Markov chain Monte Carlo sampling. A simulation study demonstrates that the proposed model has better spatial prediction performance compared to some competing models. We develop spatial maps of extreme Fosberg Fire Weather Index (FFWI), a fire threat index and discuss the wildfire risk throughout the Santa Ana region of California.
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