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Mixture models are a standard tool in statistical analysis, widely used fordensity modeling and model-based clustering. Current approaches typically modelthe parameters of the mixture components as independent variables. This canresult in overlapping or poorly separated clusters when either the number ofclusters or the form of the mixture components is misspecified. Such modelmisspecification can undermine the interpretability and simplicity of thesemixture models. To address this problem, we propose a Bayesian mixture modelwith repulsion between mixture components. The repulsion is induced by ageneralized Mat\'ern type-III repulsive point process model, obtained through adependent sequential thinning scheme on a primary Poisson point process. Wederive a novel and efficient Gibbs sampler for posterior inference, anddemonstrate the utility of the proposed method on a number of synthetic andreal-world problems.

Bayesian Repulsive Mixture Modeling with Mat\'ern Point Processes