Predicting False Discovery Proportion Under Dependence

We present a flexible framework for predicting error measures in multiple testing situations under dependence. Our approach is based on modeling the distribution of the probit transform of the p-values by mixtures of multivariate skew-normal distributions. The model can incorporate dependence among p-values and it allows for shape restrictions on the p-value density. A nonparametric Bayesian scheme for estimating the components of the mixture model is outlined and Markov chain Monte Carlo algorithms are developed. These lead to the prediction of false discovery proportion and related credible bands. An expression for the positive false discovery rate for dependent observations is also derived. The power of the mixture model in estimation of key quantities in multiple testing is illustrated by a simulation study. A dataset on kidney transplant is also analyzed using the methods developed.