Frontiers in Dependence Modeling

Date & Time: Wednesday, September 30, 2026 | 11:00 - 13:30
Place: tba
Chairs: Ariane Hanebeck, Guillermo Briseño-Sanchez

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: Structured covariance models for spatial dependence in distributional regression
Abstract: Probabilistic neural networks are commonly used for spatial data, however in parametric scenarios, estimating a full covariance matrix remains a bottleneck. The usual optimization criterion, the negative log-likelihood, behaves poorly when the true dependence structure is close to degenerate. Furthermore, it is not clear in the first place, how a high-dimensional covariance matrix can be efficiently learned.

In this talk, we consider proper scoring rules, in particular kernel scores, as estimation criteria for covariance matrices, and show that they can circumvent issues of the log-likelihood in terms of robustness. To make estimation feasible in high dimensions, we parameterize the dependence in a spectral basis, where stationary correlation becomes diagonal and heteroscedastic marginal variances can be separated from the correlation structure itself. This gives a family of models interpolating between dependency structures at near-linear cost, which can be adapted to different domains and transformations. We illustrate the behaviour of the resulting estimators on controlled simulations and on spatially structured data.

Speaker: Ferdinand Buchner (Technical University of Munich) 
Title: Covariate-Dependent Modeling with Rosenblatt Vine Copulas
Abstract: Vine copulas are flexible tools for modeling complex dependence structures among multiple variables. However, standard vine copula models typically assume a static dependence structure and therefore cannot directly capture how dependence changes with external covariates. We introduce Rosenblatt vine copulas, a nonparametric framework for modeling covariate-dependent multivariate distributions. The model decomposes the joint distribution into bivariate copulas that are estimated through univariate conditional density estimators. This construction enables the use of flexible regression and machine-learning methods while avoiding the specification of parametric copula families. We discuss the construction and estimation of Rosenblatt vine copulas and explore their ability to capture covariate-dependent dependence structures in numerical experiments. We further illustrate their potential for multivariate probabilistic forecasting.

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.