The Annals of Statistics

A multivariate empirical Bayes statistic for replicated microarray time course data

Yu Chuan Tai and Terence P. Speed

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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 2-statistic, a variant of the one-sample Hotelling T2-statistic. Both the MB-statistic and 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 MB-statistics and 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.

Article information

Ann. Statist. Volume 34, Number 5 (2006), 2387-2412.

First available in Project Euclid: 23 January 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62C12: Empirical decision procedures; empirical Bayes procedures 92D10: Genetics {For genetic algebras, see 17D92}

Microarray time course longitudinal multivariate empirical Bayes moderation gene ranking replication


Tai, Yu Chuan; Speed, Terence P. A multivariate empirical Bayes statistic for replicated microarray time course data. Ann. Statist. 34 (2006), no. 5, 2387--2412. doi:10.1214/009053606000000759.

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