I am interested in developing statistical methodology in the areas of multiple comparisons, replicability analysis, observational studies and nonparametric statistics, with applications to bioinformatics and functional Magnetic Resonance Imaging (fMRI).
Multiple comparisons and replicability analysis -
Analysis of high dimensional data, common in genomics applications and in fMRI research, has to take into consideration the severe multiple comparisons problem. In my research I develop testing strategies that first examine families of hypotheses, e.g. gene set hypotheses, and then individual hypotheses within these families, e.g. gene hypotheses. I develop analysis strategies for establishing replicability of findings when more than one study with high dimensional data is available that examines the same or a similar problem.
Observational studies -
For observational high dimensional studies, I address the problem of hidden bias by examining sensitivity analysis methods for different testing strategies.
Nonparametric statistics -
I am developing a new innovative method for tackling one of the most basic problems of statistics - are two random vectors dependent? Moreover, I plan to generalize and modify this method for many other basic problems such as the two sample problem, conditional independence and more.