Frontiers in Dependence Modeling

Abstract: 

Dependence modeling has evolved into a cornerstone of modern statistics. It provides the necessary tools to move beyond simple linear correlations and Gaussian assumptions toward a comprehensive understanding of complex, possibly non-linear multivariate relationships. Hosted under the MathSEE’s initiative to foster interdisciplinary discussion, this mini-symposium highlights recent developments in dependence modeling in both theoretical research and a diverse range of applications led by young researchers. Central to our discussion is the role of inference. On one hand, Bayesian inference offers a robust framework for uncertainty quantification and allows practitioners to integrate expert prior knowledge into complex model architectures. On the other hand, likelihood-based inference provides a computationally efficient framework that ensures scalability and statistical consistency. Ultimately, this mini-symposium serves as a collaborative forum to bridge the gap between theoretical and applied scientists, with a particular focus on statistical methods addressing challenges in science and society.

Confirmed Speakers:

Speaker: Luciana Dalla Valle (University of Turin)
Title: Bayesian model selection of vine copulas via loss-based priors
Abstract: The growing popularity of vine copulas in multivariate statistical analysis is largely driven by their ability to capture complex dependence structures. However, this flexibility comes at a cost, as the number of possible vine models grows rapidly and becomes intractable even in moderately low-dimensional settings. These limitations affect the practical applicability of current Bayesian inference and model selection approaches, effectively restricting it to problems of relatively small-dimension due to their high computational cost.

This talk addresses the still open challenge of efficient model selection and estimation in Bayesian vine methodology. We propose a novel framework for Bayesian vine copula model selection that combines loss-based model priors with the shotgun stochastic search strategy. The strength of the proposed approach is twofold: it promotes sparsity and enables fast and effective structure selection. Furthermore, our comprehensive framework jointly identifies the vine structure, selects the copula families, and estimates the model parameters. The power of the proposed approach is demonstrated via simulation studies and an application to a real dataset of EFT portfolio asset returns.

Speaker: Christopher Bülte (Ludwig Maximilian University of Munich) 
Title: TBA
Abstract: TBA

Speaker: Ferdinand Buchner (Technical University of Munich) 
Title: TBA
Abstract: TBA

Speaker: Matthias Herp (Georg August University of Göttingen)
Title: Graphical Transformation Models
Abstract: Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures semiparametrically, while maintaining interpretability through the identification of varying conditional independencies. GTMs extend multivariate transformation models by replacing the Gaussian copula with a custom-designed multivariate transformation, offering two major advantages. Firstly, GTMs can capture more complex interdependencies using penalized splines, which also provide an efficient regularization scheme. Secondly, we demonstrate how to approximately regularize GTMs towards pairwise conditional independencies using a lasso penalty, akin to Gaussian graphical models. The model's robustness and effectiveness are validated through simulations, showcasing its ability to accurately learn complex dependencies and identify conditional independencies. Additionally, the model is applied to a benchmark astrophysics dataset, where the GTM demonstrates favorable performance compared to non-parametric vine copulas in learning complex multivariate distributions.