Bayesian hypothesis testing for equality of high-dimensional means using cluster subspaces.

The classical Hotelling's T 2 test and Bayesian hypothesis tests breakdown for the problem of comparing two high-dimensional population means due to the singularity of the pooled sample covariance matrices when the model dimension p exceeds the sample size n. In this paper, we develop a simple closed-form Bayesian testing procedure based on a split-and-merge technique. Specifically, we adopt the subspace clustering technique to split the high-dimensional data into lower-dimensional random spaces so that the Bayes factor can be implemented. Then we utilize the geometric mean to merge the results of the Bayesian test to obtain a novel test statistic. We carry out simulation studies to compare the performance of the proposed test with several existing ones in the literature. Finally, two real-data applications are provided for illustrative purposes. [ABSTRACT FROM AUTHOR]