Distributed Inference for Spatial Extremes Modeling in High Dimensions

Abstract

Extreme environmental events frequently exhibit spatial and temporal dependence. These data are often modeled using Max Stable Processes (MSPs) that are computationally prohibitive to fit for as few as a dozen observations. Supposed computationally-efficient approaches like the composite likelihood remain computationally burdensome with a few hundred observations. In this article, we propose a spatial partitioning approach based on local modeling of subsets of the spatial domain that delivers computationally and statistically efficient inference. Marginal and dependence parameters of the MSP are estimated locally on subsets of observations using censored pairwise composite likelihood, and combined using a modified generalized method of moments procedure. The proposed distributed approach is extended to estimate inverted MSP models, and to estimate spatially varying coefficient models to deliver computationally efficient modeling of spatial variation in marginal parameters. We demonstrate consistency and asymptotic normality of estimators, and show empirically that our approach leads to statistically efficient estimation of model parameters. We illustrate the flexibility and practicability of our approach through simulations and the analysis of streamflow data from the U.S. Geological Survey. Supplementary materials for this article are available online.

KEYWORD:

• Bias-variance tradeoff
• Brown-Resnick process
• Divide-and-conquer
• Scalable computing

Acknowledgments

The authors thank Dr. Sankarasubramanian Arumugam of North Carolina State University for providing the streamflow data, and the reviewers and associate editor for their valuable feedback that led to a great improvement in the manuscript.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

This work was supported by grants from the National Science Foundation (DMS2152887, CBET2151651) and the National Institutes of Health (R01ES031651-01).