Random density functions with common atoms and pairwise dependence

The paper is concerned with constructing pairwise dependence between $m$ random density functions each of which is modeled as a mixture of Dirichlet process model. The key to this is how to create dependencies between random Dirichlet processes. The present paper adopts a plan previously used for creating pairwise dependence, with the simplification that all random Dirichlet processes share the same atoms. Our contention is that for all dependent Dirichlet process models, common atoms are sufficient. We show that by adopting common atoms, it is possible to compute the $L_p$ distances between all pairs of random probability measures.