Bayesian Repulsive Mixture Modeling with Matérn Point Processes

Abstract: 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.