A note on posterior sampling from Dirichlet mixture models

In this note we observe that the recent MCMC methods of Papaspiliopoulos & Roberts (2008) and Walker (2007) for Dirichlet mixture models are intrinsically con- nected and can be naturally combined to yield an algorithm which is better (in terms of mixing), faster (in terms of execution time) and easier (in terms of implementation and coding) than either of them.