Model selection for extremal dependence structures using deep learning: Application to environmental data.

This repository contains all the code, data, and resources used in our study:
“Model Selection for Extremal Dependence Structures Using Deep Learning: Application to Environmental Data.”

The goal of this research is to better understand and model the spatial dependence structure of extreme 2 m air temperatures across Iraq. We focus on selecting the most appropriate max-stable dependence structure using a deep learning approach.

Our approach uses convolutional neural networks (CNNs) to learn spatial dependence patterns from datasets simulating the max-stable models fitted to 2m air temperature phenomena. The idea is to train the networks to recognize which model and covariance structure best fit the data.

We propose two selection strategies:
• Scheme 1: A single CNN (CNN-C) that predicts both the max-stable model and its covariance function at once.
• Scheme 2: A two-stage approach, where one CNN (CNN-M) predicts the model family, and then a second CNN, selected from CNN-S (for Schlather), CNN-G (for Geometric), or CNN-E (for Extremal-t), determines the specific covariance function.

To evaluate performance, we compare these CNN-based results to a classical model selection method: the Composite Likelihood Information Criterion (CLIC). We also validate our findings using a parametric bootstrap approach based on extremal coefficients.

What the codes and dataset supports:
• Simulating spatial dependence structures under different max-stable processes
• Fitting models using composite likelihood and comparing them using CLIC
• Training CNNs to classify spatial dependence structures
• Validating model selection using extremal coefficient diagnostics
• Comparing deep learning–based selection with traditional statistical methods, e.g., CLIC