Improved Return Level Estimation via a Weighted Likelihood, Latent Spatial Extremes Model

  • Joshua HewittEmail author
  • Miranda J. Fix
  • Jennifer A. Hoeting
  • Daniel S. Cooley


Uncertainty in return level estimates for rare events, like the intensity of large rainfall events, makes it difficult to develop strategies to mitigate related hazards, like flooding. Latent spatial extremes models reduce the uncertainty by exploiting spatial dependence in statistical characteristics of extreme events to borrow strength across locations. However, these estimates can have poor properties due to model misspecification: Many latent spatial extremes models do not account for extremal dependence, which is spatial dependence in the extreme events themselves. We improve estimates from latent spatial extremes models that make conditional independence assumptions by proposing a weighted likelihood that uses the extremal coefficient to incorporate information about extremal dependence during estimation. This approach differs from, and is simpler than, directly modeling the spatial extremal dependence; for example, by fitting a max-stable process, which is challenging to fit to real, large datasets. We adopt a hierarchical Bayesian framework for inference, use simulation to show the weighted model provides improved estimates of high quantiles, and apply our model to improve return level estimates for Colorado rainfall events with 1% annual exceedance probability.

Supplementary materials accompanying this paper appear online.


Bayesian Climate Extremal coefficient Generalized extreme value distribution 



This material is based upon work supported by the National Science Foundation under Grant No. AGS–1419558 (Hewitt and Hoeting) and DMS–1243102 (Fix and Cooley). This research utilized the CSU ISTeC Cray HPC System supported by NSF Grant CNS–0923386. This work utilized the RMACC Summit supercomputer, which is supported by the National Science Foundation (Awards ACI-1532235 and ACI-1532236), the University of Colorado Boulder, and Colorado State University. The Summit supercomputer is a joint effort of the University of Colorado Boulder and Colorado State University. We also express our gratitude to Emeric Thibaud and Mathieu Ribatet. Dr. Thibaud provided code to simulate Brown–Resnick processes, and Dr. Ribatet provided a development version of the SpatialExtremes package, written for the R computing language, that implements a Gibbs sampler for the unweighted latent spatial extremes model.

Supplementary material

13253_2019_354_MOESM1_ESM.pdf (7.2 mb)
Supplementary material 1 (pdf 7384 KB)


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Copyright information

© International Biometric Society 2019

Authors and Affiliations

  1. 1. Statistics DepartmentColorado State UniversityFort CollinsUSA

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