Bayesian nonparametric multiple testing

Multiple testing, or multiplicity problems often require testing several means with the assumption of rejecting infrequently, as motivated by the need to analyze DNA microarray data. The goal is to keep the combined rate of false discoveries and non-discoveries as small as possible. A discrete approximation to a Polya tree prior that enjoys fast, conjugate updating, centered at the usual Gaussian distribution is proposed. This new technique and the advantages of this approach are demonstrated using extensive simulation and data analysis accompanied by a Java web application. The numerical studies demonstrate that this new procedure shows promising false discovery rate and estimation of key values in the mixture model with very reasonable computational speed.