## Markov Chain Sampling Methods for
Dirichlet Process Mixture Models

**Radford M. Neal,
Dept. of Statistics and Dept. of Computer Science,
University of Toronto**

Markov chain methods for sampling from the posterior distribution
of a Dirichlet process mixture model are reviewed, and two new classes
of methods are presented. One new approach is to make
Metropolis-Hastings updates of the indicators specifying which mixture
component is associated with each observation, perhaps supplemented
with a partial form of Gibbs sampling. The other new approach extends
Gibbs sampling for these indicators by using a set of auxiliary
parameters. These methods are simple to implement and are more
efficient than previous ways of handling general Dirichlet process
mixture models with non-conjugate priors.

Technical Report No. 9815, Dept. of Statistics, University of Toronto
(September 1998), 17 pages:
postscript,
pdf,
associated software.

**Associated references:**
A revised version of this technical report has appeared as the following
paper:
Neal, R. M. (2000) ``Markov chain sampling methods for Dirichlet process
mixture models'', *Journal of Computational and Graphical Statistics*
vol. 9, pp. 249-265:
abstract,
associated references,
associated software.

The following technical report describes a more elaborate algorithm
based on split-merge proposals:
Jain, S. and Neal, R. M. (2000) ``A Split-Merge Markov Chain Monte Carlo
Procedure for the Dirichlet Process Mixture Model'', Technical Report
No. 2003, Dept. of Statistics (July 2000), 32 pages:
abstract,
postscript,
pdf,
associated references.

Some earlier work of mine on models equivalent to Dirichlet process
mixtures is described in the following technical report:
Neal, R. M. (1991) ``Bayesian mixture modeling by Monte Carlo simulation'',
Technical Report CRG-TR-91-2, Dept. of Computer Science, University of Toronto,
23 pages:
abstract,
postscript, pdf,
associated references.