Abstract
This article concerns testing for equality of distribution between groups. We focus on screening variables with shared distributional features such as common support, modes and patterns of skewness. We propose a Bayesian testing method using kernel mixtures, which improves performance by borrowing information across the different variables and groups through shared kernels and a common probability of group differences. The inclusion of shared kernels in a finite mixture, with Dirichlet priors on the weights, leads to a simple framework for testing that scales well for high-dimensional data. We provide closed asymptotic forms for the posterior probability of equivalence in two groups and prove consistency under model misspecification. The method is applied to DNA methylation array data from a breast cancer study, and compares favourably to competitors when Type I error is estimated via permutation.