Title: MCMC computations for Bayesian mixture models using repulsive point processes
Authors: Mario Beraha - Politecnico di Milano, Università di Bologna (Italy) [presenting]
Raffaele Argiento - University of Torino (Italy)
Alessandra Guglielmi - Politecnico di Milano (Italy)
Jesper Moeller - Aalborg University (Denmark)
Abstract: Repulsive mixture models have recently gained popularity for Bayesian cluster detection. Compared to more traditional mixture models, there is empirical evidence suggesting that 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 point process depending on a hyperparameter - not only a Poisson or determinantal point process (DPP) as previously considered in the literature but also a repulsive point process specified by a density which depends on an intractable normalizing constant. By investigating the posterior characterization of this class of mixture models, we derive an MCMC algorithm which avoids the well-known difficulties associated with reversible jump MCMC computation. In particular, we use an ancillary variable method, which depends on perfect simulation, to overcome the problem of having a ratio of normalizing constants in the Hastings ratio when making posterior simulations for full conditional of the hyperparameter. 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 DPP or a repulsive Gibbs point process prior model.