  Discrete mixture models are routinely used for density estimation and
clustering. While conducting inferences on the cluster-specific parameters,
current frequentist and Bayesian methods often encounter problems when clusters
are placed too close together to be scientifically meaningful. Current Bayesian
practice generates component-specific parameters independently from a common
prior, which tends to favor similar components and often leads to substantial
probability assigned to redundant components that are not needed to fit the
data. As an alternative, we propose to generate components from a repulsive
process, which leads to fewer, better separated and more interpretable
clusters. We characterize this repulsive prior theoretically and propose a
Markov chain Monte Carlo sampling algorithm for posterior computation. The
methods are illustrated using simulated data as well as real datasets.
