  Large-scale multiple testing tasks often exhibit dependence, and leveraging
the dependence between individual tests is still one challenging and important
problem in statistics. With recent advances in graphical models, it is feasible
to use them to perform multiple testing under dependence. We propose a multiple
testing procedure which is based on a Markov-random-field-coupled mixture
model. The ground truth of hypotheses is represented by a latent binary Markov
random field, and the observed test statistics appear as the coupled mixture
variables. The parameters in our model can be automatically learned by a novel
EM algorithm. We use an MCMC algorithm to infer the posterior probability that
each hypothesis is null (termed local index of significance), and the false
discovery rate can be controlled accordingly. Simulations show that the
numerical performance of multiple testing can be improved substantially by
using our procedure. We apply the procedure to a real-world genome-wide
association study on breast cancer, and we identify several SNPs with strong
association evidence.
