Importance conditional sampling for Bayesian nonparametric mixtures
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Nonparametric mixture models based on the Pitman-Yor process represent a flexible tool for density estimation and clustering. Natural generalization of the popular class of Dirichlet process mixture models, they allow for more robust inference on the number of components characterizing the distribution of the data. We propose a new sampling strategy for such models, named importance conditional sampling (ICS), which combines appealing properties of existing methods, including easy interpretability and straightforward quantification of posterior uncertainty. An extensive simulation study highlights the efficiency of the proposed method which, unlike other conditional samplers, is robust to the specification of the parameters characterizing the Pitman-Yor process. The ICS also proves more efficient than marginal samplers, as soon as the sample size is not small, and, importantly, the step to update latent parameters is fully parallelizable. We further show that the ICS approach can be naturally extended to other classes of computationally demanding models, such as nonparametric mixture models for partially exchangeable data. We illustrate the behaviour of our method by analysing a rich dataset from the Collaborative Perinatal Project.
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