A Bayesian discovery procedure

Summary. The optimal discovery procedure (ODP) maximizes the expected num-ber of true positives for every fixed expected number of false positives. We show that the ODP can be interpreted as an approximate Bayes rule under a semi-parametric model. Improving the approximation leads us to a Bayesian discovery procedure (BDP), which exploits the multiple shrinkage in clusters implied by the assumed nonparametric model. We compare the BDP and the ODP estimates in a simple simulation study and in an assessment of differential gene expression between two tumor samples. We extend the setting of the ODP by discussing modifications of the loss function that lead to different single thresholding statis-tics. Finally, we provide an application of the previous arguments to dependent (spatial) data