MATH+ Junior Research Group on Statistical Inversion and Quantification of Uncertainties
Since Spring 2021 I have a junior research group at the HU Berlin funded by the MATH+ Excellence Cluster for mathematics. The topics we are interested are mainly the quantification of uncertainties in the estimation of level sets of random fields. The approach is inspired by confidence probability excursion (CoPE) sets, which have been introduced in 1 and are an active research topic I collaborate on with the group of Armin Schwartzman at the University of Californa, San Diego, and the group of Thomas Nichols at the Big Data Institute at the University of Oxford. Currently, we aim to refine and generalize the CoPE set approach in several ways to apply it not only to smooth imaging data, but also less smooth data and discrete data. Another line of generalization will be introducing different error criteria measures for CoPE sets. Currently it relies on a concept similar to the family wise error rate in multiple testing. We aim to extend it to criteria more similar to FDR control.
[1] Sommerfeld, M., Sain, S., & Schwartzman, A. (2018). Confidence regions for spatial excursion sets from repeated random field observations, with an application to climate. Journal of the American Statistical Association, 113(523), 1327-1340.