# Modeling spatial processes with unknown extremal dependence class

## TL;DR

This paper introduces a flexible spatial model that captures both asymptotic dependence and independence in environmental extremes, allowing for smooth transitions and improved extrapolation of rare events.

## Contribution

A novel parsimonious spatial model that unifies dependence classes and enables inference in moderate dimensions using censored likelihood methods.

## Key findings

- Model successfully captures a range of dependence structures.
- Application to oceanographic data demonstrates practical utility.
- Allows for accurate estimation of extreme event probabilities.

## Abstract

Many environmental processes exhibit weakening spatial dependence as events become more extreme. Well-known limiting models, such as max-stable or generalized Pareto processes, cannot capture this, which can lead to a preference for models that exhibit a property known as asymptotic independence. However, weakening dependence does not automatically imply asymptotic independence, and whether the process is truly asymptotically (in)dependent is usually far from clear. The distinction is key as it can have a large impact upon extrapolation, i.e., the estimated probabilities of events more extreme than those observed. In this work, we present a single spatial model that is able to capture both dependence classes in a parsimonious manner, and with a smooth transition between the two cases. The model covers a wide range of possibilities from asymptotic independence through to complete dependence, and permits weakening dependence of extremes even under asymptotic dependence. Censored likelihood-based inference for the implied copula is feasible in moderate dimensions due to closed-form margins. The model is applied to oceanographic datasets with ambiguous true limiting dependence structure.