## 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.

*Journal of Computational and Graphical Statistics*
vol. 9, pp. 249-265: associated software.

**Associated references:**
An earlier version of this paper was issued as the following technical
report:
Technical Report No. 9815, Dept. of Statistics, University of Toronto
(September 1998), 17 pages:
abstract,
postscript,
pdf,
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.