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**A Bayesian sparse finite mixture model for clustering data from a heterogeneous population.**
*(English)*
Zbl 1445.62152

Summary: In this paper, we introduce a Bayesian approach for clustering data using a sparse finite mixture model (SFMM). The SFMM is a finite mixture model with a large number of components \(k\) previously fixed where many components can be empty. In this model, the number of components \(k\) can be interpreted as the maximum number of distinct mixture components. Then, we explore the use of a prior distribution for the weights of the mixture model that take into account the possibility that the number of clusters \(k_{\mathbf{c}}\) (e.g., nonempty components) can be random and smaller than the number of components \(k\) of the finite mixture model. In order to determine clusters we develop a MCMC algorithm denominated Split-Merge allocation sampler. In this algorithm, the split-merge strategy is data-driven and was inserted within the algorithm in order to increase the mixing of the Markov chain in relation to the number of clusters. The performance of the method is verified using simulated datasets and three real datasets. The first real data set is the benchmark galaxy data, while second and third are the publicly available data set on Enzyme and Acidity, respectively.

### MSC:

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

62F15 | Bayesian inference |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

62P35 | Applications of statistics to physics |

85A35 | Statistical astronomy |

85A05 | Galactic and stellar dynamics |

### Keywords:

mixture model; Bayesian approach; Gibbs sampling; Metropolis-Hastings algorithm; split-merge update### Software:

AS 136
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\textit{E. F. Saraiva} et al., Braz. J. Probab. Stat. 34, No. 2, 323--344 (2020; Zbl 1445.62152)

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