[Paper Review] A semiparametric Bayesian model for spatiotemporal extremes

Arnab Hazra, Brian J. Reich+2 more|arXiv (Cornell University)|Dec 31, 2018

Spatial and Panel Data AnalysisEconomics, Econometrics and Finance4 citations

TL;DR

This paper proposes a semiparametric Bayesian model using a Dirichlet process mixture of spatial skew-t processes to jointly model bulk and extreme values in spatial data, allowing for nonstationary mean and covariance, nonzero asymptotic dependence, and probabilistic clustering of extremes. The method improves spatial prediction over competitors and is applied to map extreme Fosberg Fire Weather Index across California's Santa Ana region.

ABSTRACT

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.

Motivation & Objective

• Address the limitations of threshold-based extreme value models that exclude non-extreme but large events from analysis.
• Model both bulk and extreme distributions simultaneously with separate spatial dependence parameters.
• Incorporate nonstationary mean and covariance structures to reflect complex spatial patterns in extreme events.
• Enable nonzero asymptotic dependence in extremes to better represent spatial extremal dependence.
• Develop a probabilistic clustering approach for extreme observations to improve spatial prediction and risk assessment.

Proposed method

• Use a Dirichlet process mixture of spatial skew-t processes to flexibly model the full marginal distribution, including bulk and extremes.
• Allow separate parameters to control spatial dependence in the bulk and extreme regions of the distribution.
• Incorporate nonstationary mean and covariance functions through flexible basis expansions or covariates.
• Model extremal dependence via a spatially varying dependence structure that supports nonzero asymptotic dependence.
• Apply Markov chain Monte Carlo (MCMC) sampling for posterior inference on model parameters and latent cluster assignments.
• Cluster extreme observations probabilistically to identify spatial patterns of extreme events and their dependence structure.

Experimental results

Research questions

• RQ1 Can a unified model jointly capture bulk and extreme behavior in spatial data with flexible dependence structures?
• RQ2 How does the proposed model perform in spatial prediction compared to existing models for extremes?
• RQ3 To what extent does probabilistic clustering of extreme events improve modeling of spatial extremal dependence?
• RQ4 How well does the model capture nonstationary spatial trends and nonzero asymptotic dependence in extreme values?
• RQ5 What insights does the model provide for wildfire risk mapping using the Fosberg Fire Weather Index?

Key findings

• The proposed model demonstrates superior spatial prediction performance compared to competing models in the simulation study.
• The model successfully captures nonstationary spatial trends in both bulk and extreme regions of the distribution.
• The inclusion of nonzero asymptotic dependence allows for more realistic modeling of spatial extremal dependence.
• Probabilistic clustering of extreme events reveals coherent spatial patterns of high fire risk in the Santa Ana region.
• Spatial maps of extreme Fosberg Fire Weather Index generated by the model highlight elevated wildfire risk in specific sub-regions of California.
• The model enables analysis of large, non-extreme events that would otherwise be excluded in threshold-based approaches.