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Bayesian density estimation and model selection using nonparametric hierarchical mixtures

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  • Argiento, Raffaele
  • Guglielmi, Alessandra
  • Pievatolo, Antonio

Abstract

A class of nonparametric hierarchical mixtures is considered for Bayesian density estimation. This class, namely mixtures of parametric densities on the positive reals with a normalized generalized gamma process as mixing measure, is very flexible in the detection of clusters in the data. With an almost sure approximation of the posterior trajectories of the mixing process a Markov chain Monte Carlo algorithm is run to estimate linear and nonlinear functionals of the predictive distributions. The best-fitting mixing measure is found by minimizing a Bayes factor for parametric against nonparametric alternatives. Simulated and historical data illustrate the method, finding a trade-off between the best-fitting model and the correct identification of the number of components in the mixture.

Suggested Citation

  • Argiento, Raffaele & Guglielmi, Alessandra & Pievatolo, Antonio, 2010. "Bayesian density estimation and model selection using nonparametric hierarchical mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 816-832, April.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:4:p:816-832
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    References listed on IDEAS

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    3. Zarepour, Mahmoud & Labadi, Luai Al, 2012. "On a rapid simulation of the Dirichlet process," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 916-924.
    4. Stefano Favaro & Antonio Lijoi & Igor Prunster, 2011. "Asymptotics for a Bayesian nonparametric estimator of species richness," Quaderni di Dipartimento 144, University of Pavia, Department of Economics and Quantitative Methods.

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