  Employing nonparametric methods for density estimation has become routine in
Bayesian statistical practice. Models based on discrete nonparametric priors
such as Dirichlet Process Mixture (DPM) models are very attractive choices due
to their flexibility and tractability. However, a common problem in fitting
DPMs or other discrete models to data is that they tend to produce a large
number of (sometimes) redundant clusters. In this work we propose a method that
produces parsimonious mixture models (i.e. mixtures that discourage the
creation of redundant clusters), without sacrificing flexibility or model fit.
This method is based on the idea of repulsion, that is, that any two mixture
components are encouraged to be well separated. We propose a family of
d-dimensional probability densities whose coordinates tend to repel each other
in a smooth way. The induced probability measure has a close relation with
Gibbs measures, graph theory and point processes. We investigate its global
properties and explore its use in the context of mixture models for density
estimation. Computational techniques are detailed and we illustrate its
usefulness with some well-known data sets and a small simulation study.

Methodology