Likelihood-based inference for max-stable processes

TL;DR

This paper introduces a composite-likelihood approach for likelihood-based inference of max-stable processes, enabling more practical and flexible modeling of spatial extremes with applications to U.S. precipitation data.

Contribution

It develops a new composite-likelihood method for max-stable processes that allows joint modeling of marginal and dependence parameters efficiently.

Findings

Method performs reliably in simulations

Enables joint modeling of marginal and dependence parameters

Applied successfully to U.S. precipitation extremes

Abstract

The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so likelihood-based methods remain far from providing a complete and flexible framework for inference. In this article we develop inferentially practical, likelihood-based methods for fitting max-stable processes derived from a composite-likelihood approach. The procedure is sufficiently reliable and versatile to permit the simultaneous modeling of marginal and dependence parameters in the spatial context at a moderate computational cost. The utility of this methodology is examined via simulation, and illustrated by the analysis of U.S. precipitation extremes.