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 centers" 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. Supplementary files for this article are available online.

(2022). MCMC Computations for Bayesian Mixture Models Using Repulsive Point Processes [journal article - articolo]. In JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS. Retrieved from http://hdl.handle.net/10446/227952

MCMC Computations for Bayesian Mixture Models Using Repulsive Point Processes

Argiento, Raffaele;
2022

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 centers" 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. Supplementary files for this article are available online.
articolo
Beraha, Mario; Argiento, Raffaele; Moller, Jesper; Guglielmi, Alessandra
(2022). MCMC Computations for Bayesian Mixture Models Using Repulsive Point Processes [journal article - articolo]. In JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS. Retrieved from http://hdl.handle.net/10446/227952
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Descrizione: “This is an Accepted Manuscript version of the following article, accepted for publication in Journal of Computational and Graphical Statistics "Mario Beraha, Raffaele Argiento, Jesper Møller & Alessandra Guglielmi (2022) MCMC Computations for Bayesian Mixture Models Using Repulsive Point Processes, Journal of Computational and Graphical Statistics, 31:2, 422-435, DOI: 10.1080/10618600.2021.2000424". It is deposited under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.”
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/227952
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