Exact and efficient two-sample tests in the context of gene expression analysis

Comparing gene expression levels (or various other cell properties) across distinct sets of cells is a routine procedure to detect potential differential expression. Traditionally, analysis has focused on changes in locations, for which standard methods like the Kolmogorov-Smirnov and Mann-Whitney tests perform favorably. Recently, however, alternative and more complex expression patterns (e.g., changes in scale, correlation, or multi-modal structure) have been encountered increasingly, necessitating the design of more targeted two-sample tests. This talk will describe a framework for constructing multivariate, nonparametric two-sample tests that are efficient against user-specified (composite) alternatives, yet remain exact for small sample sizes (which, due to high heterogeneity in cell counts, is desirable for differential expression analysis), by extending so-called linear rank statistics to multivariate sample and parameter spaces.