We propose a Bayesian method for multiple hypothesis testing in ran-
dom e®ects models that uses Dirichlet process (DP) priors for a nonparametric
treatment of the random e®ects distribution. We consider a general model for-
mulation which accommodates a variety of multiple treatment conditions. A key
feature of our method is the use of a product of spiked distributions, i.e., mixtures
of a point-mass and continuous distributions, as the centering distribution for the
DP prior. Adopting these spiked centering priors readily accommodates sharp
null hypotheses and allows for the estimation of the posterior probabilities of such
hypotheses. Dirichlet process mixture models naturally borrow information across
objects through model-based clustering while inference on single hypotheses aver-
ages over clustering uncertainty. We demonstrate via a simulation study that our
method yields increased sensitivity in multiple hypothesis testing and produces a
lower proportion of false discoveries than other competitive methods. While our
modeling framework is general, here we present an application in the context of
gene expression from microarray experiments. In our application, the modeling
framework allows simultaneous inference on the parameters governing di®erential
expression and inference on the clustering of genes. We use experimental data on
the transcriptional response to oxidative stress in mouse heart muscle and compare
the results from our procedure with existing nonparametric Bayesian methods that
provide only a ranking of the genes by their evidence for di®erential expression.