Models with products of Dirichlet processes

Nonparametric Bayesian models are often preferred over parametric models due to their superior flexibility in interpreting data. A strong motivation for the use of these models is the desire of avoiding the assumptions that are necessary for parametric models. A prominent place in Bayesian nonparametrics is played by the Dirichlet process, which is defined by a base measure and a concentration parameter. In this paper, we propose the construction of models based on products of Dirichlet processes and corresponding mixture models. We show how these processes can be used for classification of data with shared features. The proposed processes are different from the recently introduced hierarchical Dirichlet processes. We show the use of the proposed model on classification of multivariate time series and demonstrate its performance with computer simulations.