Distributional copula regression for space-time data
A07 develops novel models for multivariate spatio-temporal data using distributional copula regression. Of particular interest are tests for the significance of predictors and automatic variable selection using Bayesian selection priors. In the long run, the project will consider computationally efficient modeling of non-stationary dependencies using stochastic partial differential equations.
Project Leaders
Prof. Dr. Holger Dette
Faculty of Mathematics - Chair of Stochastics
Ruhr University Bochum
Prof. Dr. Nadja Klein
Department of Informatics - Scientific Computing Center
Karlsruhe Institute of Technology
Summary
Modeling dependencies in space-time data is of interest for several projects of TRR 391 and copulas are an important mathematical tool to capture such potentially complex associations. In this project, we will develop novel models for multivariate spatio-temporal data based on copulas and distributional regression. In particular we leverage the potential of statistical testing and Bayesian shrinkage priors to induce sparse yet flexibly varying dependence structures between multiple outcomes that are observed over space and time. With the help of distributional regression it will be possible to describe the entire conditional distributions - including the dependence structure - as functions of space, time and potentially further covariates. To find a reasonable model we will construct statistical tests to determine the copula specification on the one hand, and complement these on the other hand by automatic variable selection using Bayesian variable selection priors. The latter will be particularly appealing to allow for hierarchical model specifications and modular estimation in potentially high-dimensional spatio-temporal copula regression models. Estimation is planned to be conducted by variational inference and generalized Bayesian methods. In a long-term perspective we will consider modeling the dependence structures non-stationary, handle irregularly observed and missing space-time data and leverage the potential of deep learning methods to capture high-dimensional interactions of the joint covariate, space and time domains more thoroughly.
Azadkia, M., Dette, H. (2026). Kernel estimation of Chatterjee's dependence coefficient. arXiv. DOI: 10.48550/arXiv.2602.14206.
Bai, L., Dette, H., Yuan, Z. (2026). Validating spatial-temporal separability for stationary processes. arXiv. DOI: 10.48550/arXiv.2603.26369.
Bastian, P., Dette, H., Dunsche, M. (2025). Differentially private testing for relevant dependencies in high dimensions. arXiv. DOI: 10.48550/arXiv.2511.17167.
Bianco, N., Klein, N. (2026). Scalable and robust spatial prediction via multi-resolution ensembles of predictive processes. arXiv. DOI: 10.48550/arXiv.2603.19977.
Bücher, A., Dette, H. (2025). On the lack of weak continuity of Chatterjee's correlation coefficient. To appear in Statistical Science. Already available on arXiv. DOI: 10.48550/arXiv.2410.11418.
Dette, H., Dörr, P. (2026). Testing for correct model specification in copula regression models. arXiv. DOI: 10.48550/arXiv.2607.14930.
Dette, H., Kroll, M. (2024). Detecting practically significant dependencies in infinite dimensional data via distance correlations. arXiv. DOI: 10.48550/arXiv.2411.16177.
Dette, H., Kühnert, S. (2026). A spectral based coefficient of determination for the fit of an MA(q) model. arXiv. DOI: 10.48550/arXiv.2606.18445.
Dette, H., Möllenhoff, K., Wied, D. (2025). Practically significant differences between conditional distribution functions. arXiv. DOI: 10.48550/arXiv.2506.06545.
Fuchs, T., Kalinke, F., Klein, N. (2026). QDSB: Quantized diffusion Schrödinger bridges. arxiv. DOI: 10.48550/arXiv.2605.11983.
Fuchs, T., Klein, N. (2026). Amortized variational inference for partial-label learning: A probabilistic approach to label disambiguation. To appear in ICML 2026. Already available on arXiv. DOI: 10.48550/arXiv.2510.21300.
Groenke, B. R., Wessel, J., Miersch, P., Klein, N., Zscheischler, J. (2026). Stochastic weather generation for scenario-neutral impact assessments using simulation-based inference. To appear in Journal of Geophysical Research – Machine Learning and Computation. Already available as pdf.
Kaiser, S., Klein, N., Kaack, L. (2025). From counting stations to city-wide estimates: data-driven bicycle volume extrapolation. Environmental Data Sciene 4 (e13), 1–43. DOI: 10.1017/eds.2025.5.
Klein, N., Bianco, N. (2025). Contributed discussion on "Model uncertainty and missing data: An objective Bayesian perspective" by Garcia-Donato et al. Bayesian Analysis 20(4), 1677–1778. DOI: 10.1214/25-BA1531.
Klein, N., Lee, A. W. Q., Mateu, J. (2026). Bayesian effect selection for additive quantile regression with an application to air pollution thresholds. arXiv. DOI: 10.48550/arXiv.2606.12164.
Kock, L., Klein, N., Nott, D.J. (2025). Deep mixture of linear mixed models for complex longitudinal data. Statistics in Medicine 44 (23-24), e70288. DOI: 10.1002/sim.70288.
Kock, L., Rodrigues, G. S., Sisson, S. A., Klein, N., Nott, D. J. (2026). Calibrating multivariate regression with localized PIT mappings. Journal of Computational and Graphical Statistics. DOI: 10.1080/10618600.2026.2652919.
Labanca, F., Gottard, A., Klein, N. (2026). Copula-based models for spatially dependent cylindrical data. arXiv. DOI: 10.48550/arXiv.2602.05778.
Lütke Schwienhorst, B., Klein, N., Lederer, J. (2026). Diffusion-based denoising beats vanilla score matching in parameter estimation: A theoretical explanation. arXiv. DOI: 10.48550/arXiv.2605.22950.
Marmolejo-Ramos, F., Tirado, C., Yamada, Y., Sasaki, K., Hinojosa, J., Parzuchowski, M., Marszalek, M., Tejada, J., Rečka, K., Klein, N., Briseño-Sánchez, G., Kundrát, J. (2026). The vertical symphony: How pitch perception shapes spatial and affective mapping across different countries. Cognitive Processing 27, 677–692. DOI: 10.1007/s10339-026-01364-2.
Strömer, A., de Carvalho, M., Klein, N., Mayr, A. (2025). Modeling joint extreme events via boosting distributional copula regression. Proceedings of the 39th International Workshop on Statistical Modelling, Volume 1. pdf.
Wenkel, J. M., Smith, M. S., Klein, N. (2026). Bayesian additive regression tree copula processes for scalable distributional prediction. arXiv. DOI: 10.48550/arXiv.2601.04913.
Yuan, Z., Dette, H. (2025). Exponential inequalities for some mixing processes and dynamic systems. arXiv. DOI: 10.48550/arXiv.2208.11481.