Improved return level estimation via a weighted likelihood, latent spatial extremes model

TL;DR

This paper introduces a weighted likelihood approach within a hierarchical Bayesian framework to improve return level estimates for rare spatial extreme events, addressing model misspecification issues in latent spatial extremes models.

Contribution

It proposes a simple, effective method to incorporate extremal dependence information into latent spatial extremes models without complex max-stable process fitting.

Findings

Weighted likelihood improves high quantile estimates

Method enhances return level accuracy for rainfall extremes

Application to Colorado rainfall data demonstrates practical benefits

Abstract

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 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.