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Bayesian Repulsive Gaussian Mixture Model
We develop a general class of Bayesian repulsive Gaussian mixture models that
encourage well-separated clusters, aiming at reducing potentially redundant
components produced by independent priors for locations (such as the Dirichlet
process). The asymptotic results for the posterior distribution of the proposed
models are derived, including posterior consistency and posterior contraction
rate in the context of nonparametric density estimation. More importantly, we
show that compared to the independent prior on the component centers, the
repulsive prior introduces additional shrinkage effect on the tail probability
of the posterior number of components, which serves as a measurement of the
model complexity. In addition, an efficient and easy-to-implement
blocked-collapsed Gibbs sampler is developed based on the exchangeable
partition distribution and the corresponding urn model. We evaluate the
performance and demonstrate the advantages of the proposed model through
extensive simulation studies and real data analysis. The R code is available at
https://drive.google.com/open?id=0B_zFse0eqxBHZnF5cEhsUFk0cVE
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