Anisotropic determinantal point processes and their application in Bayesian mixtures

Repulsive mixture models have recently gained visibility in Bayesian statistics. In such models, a finite repulsive point process is assumed as prior distribution for the number of components and component-specific parameters. We assume a determinantal point process as such prior, proposing a simple construction of anisotropic determinantal point processes, that can better characterize repulsion when data have different scales along the axes. In turn, this produces better cluster estimates. We discuss the model on simulated data.