Nesta sessão, apresentada por Lídia André (PhD), serão discutidos novos modelos de dependência capazes de representar simultaneamente as regiões centrais e extremas de distribuições multivariadas, com especial ênfase em métodos de inferência modernos baseados em redes neuronais.
Abstract: When an accurate representation of multivariate data is required across both the body (described by non-extreme observations) and the tail (defined by the extreme observations) regions, it is crucial to have a model that is able to characterise the joint behaviour across both regions. In this work, we propose dependence models that represent the entire distribution without the need to explicitly define each region. We do so by constructing copulas that are based on mixture distributions defined on the full support of the data. For such models, we derive (sub)-asymptotic dependence properties for specific model configurations, and show that they are flexible in capturing a broad range of extremal dependence structures through simulation studies. Motivated by the computational resources required to evaluate the likelihood function of the proposed models, we also explore likelihood-free approaches that use neural networks to perform inference. In particular, we assess the performance of neural Bayes estimators in estimating the model parameters, both for one of the models introduced for the joint body and tail, and further complex extremal dependence models. We also propose a neural Bayes classifier for model selection. In this way, we provide a toolbox for simple fitting and model selection of complex extremal dependence models.
* Joint works with: Jennifer Wadsworth, Jonathan Tawn, Raphaël Huser and Adrian O’Hagan
Short bio: Lídia André received her PhD in Statistics in 2025 from Lancaster University, and later held a postdoctoral research position in University of Namur, Belgium. Her research interests mainly lie in multivariate extreme value theory and computational statistics with environmental applications. Part of her research is also focused on developing statistical software for open-source, user friendly, applicability, and she has strong computational skills in R and Julia.