MCMC computations for Bayesian mixture models using repulsive point processes

TL;DR

This paper introduces a new MCMC framework for Bayesian mixture models with repulsive priors, avoiding reversible jump complexities, and demonstrates its efficiency and advantages through simulations and sociological data analysis.

Contribution

It develops a general MCMC algorithm for repulsive mixture models that bypasses reversible jump difficulties using an ancillary variable approach.

Findings

The new method outperforms existing approaches in simulations.

It effectively handles intractable normalizing constants.

Demonstrates practical advantages in sociological data analysis.

Abstract

Repulsive mixture models have recently gained popularity for Bayesian cluster detection. Compared to more traditional mixture models, repulsive mixture models produce a smaller number of well separated clusters. The most commonly used methods for posterior inference either require to fix a priori the number of components or are based on reversible jump MCMC computation. We present a general framework for mixture models, when the prior of the `cluster centres' is a finite repulsive point process depending on a hyperparameter, specified by a density which may depend on an intractable normalizing constant. By investigating the posterior characterization of this class of mixture models, we derive a MCMC algorithm which avoids the well-known difficulties associated to reversible jump MCMC computation. In particular, we use an ancillary variable method, which eliminates the problem of having intractable normalizing constants in the Hastings ratio. The ancillary variable method relies on a perfect simulation algorithm, and we demonstrate this is fast because the number of components is typically small. In several simulation studies and an application on sociological data, we illustrate the advantage of our new methodology over existing methods, and we compare the use of a determinantal or a repulsive Gibbs point process prior model.