An Approximate Bayes Factor-Based MANOVA Test Using Random Projection with Application in Cancer Genomics

• Activity Number: 48 - Academics Industry Perspectives on Cancer Data Innovations: Simultaneous Inference, Inconsistency, and Clinical Response
• Type: Topic-Contributed
• Date/Time: Sunday, August 8, 2021 : 3:30 PM to 5:20 PM
• Sponsor: Biometrics Section
• Author(s): Roger Zoh*
• Companies: Indiana University
• Keywords: Bayes factors; Random Projections

Abstract

High-dimensional mean testing problem remain a very active research area. However most of the focus has been on the case of independent two-group mean. We develop a Bayes factor(BF) based MANOVA test for comparing two or more population means in high dimensional settings. In ‘large-p-small-n’ settings, Bayes factors based on proper priors require eliciting a large and complex p×p covariance matrix, whereas Bayes factors based on Jeffrey’s prior suffer the same impediment as the other classical test statistics as they involve inversion of ill-formed sample covariance matrices. To circumvent this limitation, we propose that the Bayes factor be based on lower dimensional random projections of the high dimensional data vectors. We investigate various approaches of choosing the prior under the alternative. The final test statistic is based on an ensemble of Bayes factors corresponding to multiple replications of randomly projected data. We show that the test has appropriate size and is consistent. We demonstrate the efficacy of the approach through simulated and real data examples.