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Biostatistics Advance Access published online on March 24, 2006
Biostatistics, doi:10.1093/biostatistics/kxj032
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© The Author 2006. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org
Received December 15, 2005
Revised March 10, 2006
Accepted March 23, 2006

Article

A Laplace Mixture Model for Identification of Differential Expression in Microarray Experiments

Debjani Bhowmick 1, A. C. Davison 1 *, and Darlene R. Goldstein 1

1 Ecole Polytechnique Fédérale de Lausanne, Institute of Mathematics, EPFL-FSB-IMA, Station 8, CH-1015 Lausanne, Switzerland

* To whom correspondence should be addressed.
A. C. Davison, E-mail: anthony.davison{at}epfl.ch


  Abstract

Microarrays have become an important tool for studying the molecular basis of complex disease traits and fundamental biological processes. A common purpose of microarray experiments is the detection of genes that are differentially expressed under two conditions, such as treatment versus control, or wild-type versus knock-out.

We introduce a Laplace mixture model as a long-tailed alternative to the normal distribution when identifying differentially expressed genes in microarray experiments, and provide an extension to asymmetric over- or under- expression. This model permits greater flexibility than models in current use as it has the potential, at least with sufficient data, to accommodate both whole genome and restricted coverage arrays.

We also propose a REML-type approach to hyperparameter estimation which is equally applicable in the Normal mixture case.

The Laplace model appears to give some improvement in fit to data, although simulation studies show that our method performs similarly to several other statistical approaches to the problem of identification of differential expression.

Keywords: Laplace distribution; Marginal likelihood; Microarray experiment; Mixture model; REML.
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