Exploration and Inference in Spatial Extremes Using Empirical Basis Functions
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Statistical methods for inference on spatial extremes of large datasets are yet to be developed. Motivated by standard dimension reduction techniques used in spatial statistics, we propose an approach based on empirical basis functions to explore and model spatial extremal dependence. Based on a low-rank max-stable model, we propose a data-driven approach to estimate meaningful basis functions using empirical pairwise extremal coefficients. These spatial empirical basis functions can be used to visualize the main trends in extremal dependence. In addition to exploratory analysis, we describe how these functions can be used in a Bayesian hierarchical model to model spatial extremes of large datasets. We illustrate our methods on extreme precipitations in eastern USA.
Supplementary materials accompanying this paper appear online
KeywordsDimension reduction Max-stable process Non-stationary data analysis
The authors acknowledge Dan Cooley and Michael Wehner for their helpful suggestions on the manuscript. The authors’ work was partially supported by Grants from the Department of the Interior (14-1-04-9), National Institutes of Health (R21ES022795-01A1), the US Environmental Protection Agency (R835228), the National Science Foundation (1107046). The calculations have been performed using the facilities of the Scientific IT and Application Support Center of EPFL.
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