Two‐group Poisson‐Dirichlet mixtures for multiple testing

The simultaneous testing of multiple hypotheses is common to the analysis of high‐dimensional data sets. The two‐group model, first proposed by Efron, identifies significant comparisons by allocating observations to a mixture of an empirical null and an alternative distribution. In the Bayesian nonparametrics literature, many approaches have suggested using mixtures of Dirichlet Processes in the two‐group model framework. Here, we investigate employing mixtures of two‐parameter Poisson‐Dirichlet Processes instead, and show how they provide a more flexible and effective tool for large‐scale hypothesis testing. Our model further employs nonlocal prior densities to allow separation between the two mixture components. We obtain a closed‐form expression for the exchangeable partition probability function of the two‐group model, which leads to a straightforward Markov Chain Monte Carlo implementation. We compare the performance of our method for large‐scale inference in a simulation study and illustrate its use on both a prostate cancer data set and a case‐control microbiome study of the gastrointestinal tracts in children from underdeveloped countries who have been recently diagnosed with moderate‐to‐severe diarrhea.