Distributed Inference for Spatial Extremes Modeling in High Dimensions.

Area of Science:

• Environmental Science
• Statistics
• Extreme Value Theory

Background:

• Extreme environmental events often display complex spatial and temporal dependencies.
• Traditional max stable processes (MSPs) are computationally intensive, limiting their application to small datasets.
• Existing efficient methods like composite likelihood are still burdensome for larger datasets.

Purpose of the Study:

• To develop a computationally and statistically efficient method for fitting max stable processes (MSPs) to large spatial datasets of extreme environmental events.
• To enable robust inference for both marginal and dependence parameters of MSPs.
• To extend the methodology for analyzing inverted MSPs and spatially varying coefficient models.

Main Methods:

• A novel spatial partitioning approach is proposed, dividing the spatial domain into local subsets for modeling.
• Censored pairwise composite likelihood is used for local estimation of MSP parameters within subsets.
• A modified generalized method of moments procedure is employed to combine local estimates.
• The approach is extended to inverted MSPs and spatially varying coefficient models.

Main Results:

• The proposed distributed approach demonstrates computational and statistical efficiency.
• Consistency and asymptotic normality of the estimators are theoretically demonstrated.
• Empirical studies confirm statistically efficient parameter estimation.
• The method is shown to be flexible and practical through simulations and real-world streamflow data analysis.

Conclusions:

• The spatial partitioning approach significantly enhances the computational feasibility of fitting max stable processes (MSPs).
• This method provides a statistically efficient and practical tool for analyzing spatially dependent extreme environmental data.
• The approach offers a flexible framework for advanced spatial modeling, including inverted MSPs and spatially varying coefficients.