# Full likelihood inference for max-stable data

## TL;DR

This paper introduces a stochastic Expectation-Maximisation algorithm for full likelihood inference of max-stable multivariate distributions, significantly improving computational efficiency in high-dimensional settings.

## Contribution

It presents a novel EM-based method for max-stable data inference that outperforms direct likelihood computation in terms of speed and scalability.

## Key findings

- Demonstrates the method's effectiveness on logistic and Brown--Resnick models
- Achieves substantial reductions in computational time
- Provides strategies for further computational improvements

## Abstract

We show how to perform full likelihood inference for max-stable multivariate distributions or processes based on a stochastic Expectation-Maximisation algorithm, which combines statistical and computational efficiency in high-dimensions. The good performance of this methodology is demonstrated by simulation based on the popular logistic and Brown--Resnick models, and it is shown to provide dramatic computational time improvements with respect to a direct computation of the likelihood. Strategies to further reduce the computational burden are also discussed.