Random density functions with common atoms and pairwise dependence

The construction of pairwise dependence between m random density functions each of which is modeled as a mixture of Dirichlet processes is considered. The key to this is how to create dependencies between random Dirichlet processes. A method previously used for creating pairwise dependence is adapted, with the simplification that all random Dirichlet processes share the same atoms. The main contention is that for dependent Dirichlet processes adopting common atoms is sufficient for prediction and density estimation purposes. In addition, it is possible to compute the L2 distances between all pairs of random probability measures.