  High-dimensional mean vector testing problem for two or more groups remain a
very active research area. In these setting, traditional tests are not
applicable because they involve the inversion of rank deficient group
covariance matrix. In current approaches, this problem is addressed by simply
looking at a test assuming a sparse or diagonal covariance matrix potentially
ignoring complex dependency between features. In this paper, we develop a Bayes
factor (BF) based testing procedure for comparing two or more population means
in (very) high dimensional settings. Two versions of the Bayes factor based
test statistics are considered which are based on a Random projection (RP)
approach. RPs are appealing since they make not assumption about the form of
the dependency across features in the data. The final test statistic is based
on an ensemble of Bayes factors corresponding to multiple replications of
randomly projected data. Both proposed test statistics are compared through a
battery of simulation settings. Finally they are applied to the analysis of a
publicly available genomic single cell RNA-seq (scRNA-seq) dataset.
