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2017 ; 26
(2
): 285-295
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Identifying Mixtures of Mixtures Using Bayesian Estimation
#MMPMID28626349
Malsiner-Walli G
; Frühwirth-Schnatter S
; Grün B
J Comput Graph Stat
2017[Apr]; 26
(2
): 285-295
PMID28626349
show ga
The use of a finite mixture of normal distributions in model-based clustering
allows us to capture non-Gaussian data clusters. However, identifying the
clusters from the normal components is challenging and in general either achieved
by imposing constraints on the model or by using post-processing procedures.
Within the Bayesian framework, we propose a different approach based on sparse
finite mixtures to achieve identifiability. We specify a hierarchical prior,
where the hyperparameters are carefully selected such that they are reflective of
the cluster structure aimed at. In addition, this prior allows us to estimate the
model using standard MCMC sampling methods. In combination with a post-processing
approach which resolves the label switching issue and results in an identified
model, our approach allows us to simultaneously (1) determine the number of
clusters, (2) flexibly approximate the cluster distributions in a semiparametric
way using finite mixtures of normals and (3) identify cluster-specific parameters
and classify observations. The proposed approach is illustrated in two simulation
studies and on benchmark datasets. Supplementary materials for this article are
available online.