  This paper shows how the variational Bayes method provides a computational
efficient technique in the context of hierarchical modelling using Dirichlet
process priors, in particular without requiring conjugate prior assumption. It
shows, using the so called parameter separation parameterization, a simple
criterion under which the variational method works well. Based on this
framework, its provides a full variational solution for the Dirichlet process.
The numerical results show that the method is very computationally efficient
when compared to MCMC. Finally, we propose an empirical method to estimate the
truncation level for the truncated Dirichlet process.

Computation