  Mixture models are a standard tool in statistical analysis, widely used for
density modeling and model-based clustering. Current approaches typically model
the parameters of the mixture components as independent variables. This can
result in overlapping or poorly separated clusters when either the number of
clusters or the form of the mixture components is misspecified. Such model
misspecification can undermine the interpretability and simplicity of these
mixture models. To address this problem, we propose a Bayesian mixture model
with repulsion between mixture components. The repulsion is induced by a
generalized Mat\'ern type-III repulsive point process model, obtained through a
dependent sequential thinning scheme on a primary Poisson point process. We
derive a novel and efficient Gibbs sampler for posterior inference, and
demonstrate the utility of the proposed method on a number of synthetic and
real-world problems.
