Mathematics – Statistics Theory
Scientific paper
2007-02-23
Annals of Statistics 2006, Vol. 34, No. 5, 2387-2412
Mathematics
Statistics Theory
Published at http://dx.doi.org/10.1214/009053606000000759 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst
Scientific paper
10.1214/009053606000000759
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.
Speed Terence P.
Tai Yu Chuan
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