A07 - Statistical inference for molecules: How many, when and where?

In this project we aim to map the spatial molecular and brightness distribution of the sample for scanning microscopy such as STED, by exploiting the fact that a single molecule can emit only one photon at a time. This will build on a rigorous statistical convolution modeling of higher order photon coincidences. Based on this model we envision the development of various novel statistical inference tasks, e.g. on the number of molecules at a given spot, including the possibility to obtain information about the estimation error. On the experimental side we need to optimize and adapt the detection path of our microscopes and screen novel dyes. In summary, we aim to develop a novel automatized statistical analysis tool for scanning microscopy. The obtained molecular maps and their statistical confidence bounds will give us new insights into interesting biological phenomena.
Members of this project:

Prof. Dr. Axel Munk
Dr. Katharina Proksch

Associate projects:
Dr. Frank Werner

Frahm, L., Keller-Findeisen, J., Alt, P., Schnorrenberg, S., del Álamo Ruiz, M., Aspelmeier, T., Munk, A., Jakobs, S. and Hell, S. (2019)
Molecular contribution function in RESOLFT nanoscopy
Opt. Express, 27(15): 21956, DOI:org/10.1364/OE.27.021956

Proksch, K., Werner F. and Munk, A. (2018)
Multiscale scanning in inverse problems
Ann. Statist., 46(6B): 3569-3602, DOI:org/10.1214/17-AOS1669

Li, H. and Werner, F. (2018)
Empirical Risk Minimization as Parameter Choice Rule for General Linear Regularization Methods

Werner, F. (2018)
Adaptivity and Oracle Inequalities in Linear Statistical Inverse Problems: a (numerical) survey. In: New Trends in Parameter Identification for Mathematical Models
Zubelli, B. H. L. P.Springer,: 291-316, DOI:10.1007/978-3-319-70824-9_15

Dunker, F., Eckle, K., Proksch, K. and Schmidt-Hieber, J. (2017)
Tests for qualitative features in the random coefficients model
DOI: arXiv:1704.01066

Schneider, L., Schmidt-Hieber, J., Staudt, T., Krajina, A., Aspelmeier T. and Munk, A. (2018)
Posterior consistency for in the binomial problem with both parameters unknown - with applications to quantitative nanoscopy

Munk, A. and Werner, F. (2015)
Discussion of "Hypotheses testing by convex optimization"
Electronic Journal of Statistics, 9(2): 1720-1722

Ta, H., Keller, J., Haltmeier, M., Saka, S. K., Schmied, J., Opazo, F., Tinnefeld, P., Munk, A. and 1, S. W. H. (2015)
Mapping molecules in scanning far-field fluorescence nanoscopy
NATURE COMMUNICATIONS, 6: 1-7, DOI:10.1038/ncomms8977

Frick, K., Munk, A. and Sieling, H. (2014)
Multiscale change point inference
J. R. Stat. Soc. Ser. B (Statistical Methodol.), 76(3): 495-580, DOI:10.1111/rssb.12047