  The hierarchical Dirichlet process (HDP) has become an important Bayesian
nonparametric model for grouped data, such as document collections. The HDP is
used to construct a flexible mixed-membership model where the number of
components is determined by the data. As for most Bayesian nonparametric
models, exact posterior inference is intractable---practitioners use Markov
chain Monte Carlo (MCMC) or variational inference. Inspired by the split-merge
MCMC algorithm for the Dirichlet process (DP) mixture model, we describe a
novel split-merge MCMC sampling algorithm for posterior inference in the HDP.
We study its properties on both synthetic data and text corpora. We find that
split-merge MCMC for the HDP can provide significant improvements over
traditional Gibbs sampling, and we give some understanding of the data
properties that give rise to larger improvements.
