Resampling and model validation for spatio-temporal data

A03 employs complexity-reducing structural assumptions to construct resampling-based inference procedures and develops statistical tools to quantify deviations from such assumptions. A particular focus is on methods that allow to differentiate practically relevant and non-relevant deviations from simplifying assumptions such as, e.g., separability or low-rank approximations. In the long term, this project investigates resampling and model validation for multi-resolution approximations, high-dimensional modeling, and statistical inference for complex non-stationary spatio-temporal data.

In spatio-temporal data analysis structural assumptions on the covariance function, such as symmetry, (spatial) isotropy or various forms of separability are often imposed to improve estimation efficiency and to achieve computational benefits, such as reduced computation time and lower data storage requirements. They are rarely made because one believes these to hold exactly, but with the hope that the deviations from the postulated model are relatively small, such that the application of more efficient statistical inferential procedures tailored for the structural assumptions is possible. Therefore, in practice, one is generally confronted with the tradeoff of balancing a potentially larger bias because of overly restrictive model assumptions against a potentially smaller variance due to the additional structure imposed.

In this project, we make use of complexity-reducing structural model assumptions to develop new and more efficient resampling-based inference procedures for the analysis of spatio-temporal data. We will develop statistical methods to quantify deviations from such assumptions and construct suitable tests for model validation.  In addition to methodology for exact hypotheses (e.g. exact separability of the covariance), we will also supply methodology that allows to quantify deviations and to differentiate between practically relevant and non-relevant deviations from the postulated model assumptions. In particular, we investigate the statistical properties of these methods, such as validity or consistency, from an asymptotic point of view considering different sampling schemes in space and time.

Besides commonly used structural assumptions imposed on the covariance function such as parametric models, symmetry, (spatial) isotropy, or various forms of separability, our focus is also on complexity-reducing approaches including sparsity, low rank methods, separable expansions for covariance estimation and also nonlinear methods.