  The Dirichlet Process Mixture Model (DPMM) is a Bayesian non-parametric
approach widely used for density estimation and clustering. In this manuscript,
we study the choice of prior for the variance or precision matrix when Gaussian
kernels are adopted. Typically, in the relevant literature, the assessment of
mixture models is done by considering observations in a space of only a handful
of dimensions. Instead, we are concerned with more realistic problems of higher
dimensionality, in a space of up to 20 dimensions. We observe that the choice
of prior is increasingly important as the dimensionality of the problem
increases. After identifying certain undesirable properties of standard priors
in problems of higher dimensionality, we review and implement possible
alternative priors. The most promising priors are identified, as well as other
factors that affect the convergence of MCMC samplers. Our results show that the
choice of prior is critical for deriving reliable posterior inferences. This
manuscript offers a thorough overview and comparative investigation into
possible priors, with detailed guidelines for their implementation. Although
our work focuses on the use of the DPMM in clustering, it is also applicable to
density estimation.
