  In this paper we derive one- and two-sample multivariate empirical Bayes
statistics (the $\mathit{MB}$-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 $\mathit{MB}$-statistic and a
one-sample $\widetilde{T}{}^2$-statistic, a variant of the one-sample Hotelling
$T^2$-statistic. Both the $\mathit{MB}$-statistic and
$\widetilde{T}^2$-statistic can be used to rank genes in the order of evidence
of nonzero mean, incorporating the correlation structure across time points,
moderation and replication. We also derive the corresponding
$\mathit{MB}$-statistics and $\widetilde{T}^2$-statistics for the one-sample
problem where the null hypothesis states that the expected temporal profile is
constant, and for the two-sample problem where the null hypothesis is that two
expected temporal profiles are the same.
