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 defi ned 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 work with: Jennifer Wadsworth, Jonathan Tawn, Raphaël Huser and Adrian O’Hagan.

Since the coined question in 1986 “Can a set of weak learners create a single strong learner?”, ensemble learning has been focused on merging simple machine learning methods in order to increase predictive performance. Characteristics such as stability and diversity are important to choose these weak learners in bagging procedure. In the same field, Support Vector Models (SVM) are strong and stable learners which have been drawing the attention of the community once these models have some properties which are easy to characterize and at the same time provide an estimation process with global optimization properties. In this talk, we present the Random Machines method. A new machine learning method based on SVM ensemble learning which exposes how a set of strong learners can create a single stronger learner.

Recent years have seen remarkable progress in Monte Carlo simulation methods, driven by the integration of cutting-edge machine learning techniques such as Generative Adversarial Networks (GANs), diffusion models, and normalizing flows. These innovations enable the generation of complex, high-dimensional data, from highly realistic human faces to artistic transformations, such as converting a landscape photo into a Van Gogh-style painting. These breakthroughs, which often make headlines, capture widespread interest but remain challenging to simulate using traditional Monte Carlo techniques. GANs operate by training two networks in a competitive framework, yielding impressive results in high-dimensional sampling. Diffusion models offer a compelling alternative to Monte Carlo sampling by iteratively refining samples, reversing a noise-adding process, and producing smooth transitions critical for many applications. Normalizing flows map simple, tractable distributions (e.g., Gaussians) to complex target distributions through a sequence of invertible transformations, enabling efficient density estimation and sample generation. These advancements significantly expand the scope of Monte Carlo simulations, allowing statisticians and researchers to model more complex and non-standard distributions with greater accuracy and computational efficiency. This talk will explore these transformative methods, highlighting their principles, applications, and potential to redefine simulation in modern statistics and data science.

Neste estudo, propomos um método diagnóstico baseado em uma nova família de funções de ligação, que permite avaliar a sensibilidade de ligações simétricas (como o logit) em relação a versões assimétricas. Essa abordagem visa melhorar o ajuste de modelos de regressão binária, especialmente em contextos médicos, onde o uso da função logit é comum devido à sua interpretabilidade via razão de chances. O modelo geral proposto, estimado por métodos baseados em verossimilhança, permite substituir a ligação padrão quando inadequada. Também desenvolvemos ferramentas de influência local sob diferentes esquemas de perturbação, com ênfase na sensibilidade da função de ligação e razão de chances. Simulações de Monte Carlo e aplicações com dados médicos ilustram a utilidade da proposta, ressaltando a importância de diagnósticos estatísticos adequados na modelagem.