Dependent mixtures of Dirichlet processes

An approach to modeling dependent nonparametric random density functions is presented. This is based on the well known mixture of Dirichlet process model. The idea is to use a technique for constructing dependent random variables, first used for dependent gamma random variables. While the methodology works for an arbitrary number of dependent random densities, with each pair having their own dependent structure, the mathematics and estimation algorithm is focused on two dependent random density functions. Simulations and a real data example are presented.