B1901
Title: An approximate Bayes factor-based high dimensional MANOVA using random projections
Authors: Roger Zoh - Indiana University (United States) [presenting]
Abstract: High-dimensional mean vector testing problems for two independent groups remain an active research area. When the length of the mean vector exceeds the groups' combined sample sizes, tests based on the Mahalanobis distance degenerate since they involve the inversion of ill-formed sample covariance matrices. Most approaches in the literature overcome this limitation by imposing a structure on the covariance matrices. Unfortunately, these assumptions are often unrealistic and difficult to justify in practice. A Bayes factor (BF)-based test is proposed for comparing two or more population means in (very) high dimensional problems while making no a priori assumptions about the structure of the large unknown covariance matrices. The test is based on random projections (RPs), a popular data perturbation technique. RPs are appealing because they are easy to implement and are virtually applicable to any dependent structure between features in the data. Two versions of Bayes factor-based test statistics are considered. The final test statistic is based on an ensemble of Bayes factors corresponding to multiple replications of randomly projected data. The tests are applied to the analysis of a publicly available single-cell RNA-seq (scRNA-seq) dataset to compare gene expression between cell types.
