We discuss an interpretation of the optimal discovery procedure (ODP, Storey 2006) as an approximate Bayes rule in a nonparametric Bayesian model for multiple comparisons. An improved approximation defines a non-parametric Bayesian version of the ODP statistic (BDP). The definition includes multiple shrinkage in clusters. In a simulation study and a data analysis example we show a (small) improvement in frequentist summaries. The BDP allows easy modifications for dependence of the comparisons and other extensions of the ODP.