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Bayesian density estimation and model selection using nonparametric hierarchical mixtures

Authors
Journal
Computational Statistics & Data Analysis
0167-9473
Publisher
Elsevier
Publication Date
Volume
54
Issue
4
Identifiers
DOI: 10.1016/j.csda.2009.11.002
Disciplines
  • Computer Science

Abstract

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.

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