The investigator studies two topics concerning the analysis of mixture distributions which are relevant for the analysis of flow cytometry data. The investigator develops a rigorous theoretical basis for the inference on the mixture complexity, i.e. the number of subpopulations in the mixture. This understanding allows to develop new methodology that provides finite-sample confidence statements, is more powerful than existing techniques, yet at the same time is more generally applicable. The second topic addresses the quantitative characterization of differences in two multivariate distributions, based on samples from these distributions. The research develops methodology to detect regions where the two distributions differ, provides scientifically meaningful and interpretable descriptions of these regions, and provides confidence statements for the corresponding differences. The underlying methodology is also applicable to other problems, such as the detection of spatial clusters of disease cases.
Flow cytometry instruments are among the most widely used biomedical instruments in the world, but the lack of appropriate statistical methodology for analyzing the data generated by this instrument is a roadblock to harnessing its full potential. The investigator studies two topics that arise in the analysis of flow cytometry data, but which are also important for other applications. Those data are comprised of various subpopulations, and the investigator develops rigorous methodolgy to determine how many such subpopulations can be distinguished, and how to characterize differences in two samples that may have different numbers of subpopulations. These are important tasks for the anlysis of flow cytometry data which to date have not been satisfactorily resolved. Advances in the statistical methodology methodology for the above topics have the potential of a significant impact in biomedical research and in the clinical setting, and have furthermore important applications in the detection of spatial clusters in bio-surveillance, ecology, astronomy, and medical imaging.
