Distributed Inference for Spatial Extremes Modeling in High Dimensions

TL;DR

This paper introduces a distributed, local modeling approach for max stable processes to efficiently analyze high-dimensional spatial extremes, reducing bias and computational burden.

Contribution

It proposes a novel spatial partitioning method with local estimation and a modified GMM, improving efficiency and bias reduction in spatial extremes modeling.

Findings

Reduces bias compared to full data methods

Demonstrates computational efficiency in high dimensions

Validates approach with simulations and real data

Abstract

Extreme environmental events frequently exhibit spatial and temporal dependence. These data are often modeled using max stable processes (MSPs). MSPs are computationally prohibitive to fit for as few as a dozen observations, with supposed computationally-efficient approaches like the composite likelihood remaining computationally burdensome with a few hundred observations. In this paper, 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 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 a surprising reduction in bias of parameter estimates over a full data approach. We illustrate the flexibility and practicability of our approach through simulations and the analysis of streamflow data from the U.S. Geological Survey.