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A space‐time skew‐ t model for threshold exceedances
Author(s) -
Morris Samuel A.,
Reich Brian J.,
Thibaud Emeric,
Cooley Daniel
Publication year - 2017
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12644
Subject(s) - skew , statistical physics , space (punctuation) , physics , mathematics , computer science , statistics , astronomy , operating system
Summary To assess the compliance of air quality regulations, the Environmental Protection Agency (EPA) must know if a site exceeds a pre‐specified level. In the case of ozone, the level for compliance is fixed at 75 parts per billion, which is high, but not extreme at all locations. We present a new space‐time model for threshold exceedances based on the skew‐ t process. Our method incorporates a random partition to permit long‐distance asymptotic independence while allowing for sites that are near one another to be asymptotically dependent, and we incorporate thresholding to allow the tails of the data to speak for themselves. We also introduce a transformed AR(1) time‐series to allow for temporal dependence. Finally, our model allows for high‐dimensional Bayesian inference that is comparable in computation time to traditional geostatistical methods for large data sets. We apply our method to an ozone analysis for July 2005, and find that our model improves over both Gaussian and max‐stable methods in terms of predicting exceedances of a high level.