A multivariate empirical Bayes statistic for replicated microarray time course data

Abstract

In this paper we derive one- and two-sample multivariate empirical Bayes statistics (the MB-statistics) to rank genes in order of interest from longitudinal replicated developmental microarray time course experiments. We first use conjugate priors to develop our one-sample multivariate empirical Bayes framework for the null hypothesis that the expected temporal profile stays at 0. This leads to our one-sample MB-statistic and a one-sample T̃2-statistic, a variant of the one-sample Hotelling T 2-statistic. Both the MB-statistic and T̃2-statistic can be used to rank genes in the order of evidence of nonzero mean, incorporating the correlation structure across time points, moderation and replic..