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Nonparametric Bayesian inference for multivariate density functions using Feller priors

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  • Xiang Zhang
  • Yanbing Zheng

Abstract

Multivariate density estimation plays an important role in investigating the mechanism of high-dimensional data. This article describes a nonparametric Bayesian approach to the estimation of multivariate densities. A general procedure is proposed for constructing Feller priors for multivariate densities and their theoretical properties as nonparametric priors are established. A blocked Gibbs sampling algorithm is devised to sample from the posterior of the multivariate density. A simulation study is conducted to evaluate the performance of the procedure.

Suggested Citation

  • Xiang Zhang & Yanbing Zheng, 2014. "Nonparametric Bayesian inference for multivariate density functions using Feller priors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 321-340, June.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:2:p:321-340
    DOI: 10.1080/10485252.2014.894512
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    References listed on IDEAS

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    1. Stephen G. Walker & Paul Damien & PuruShottam W. Laud & Adrian F. M. Smith, 1999. "Bayesian Nonparametric Inference for Random Distributions and Related Functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 485-527.
    2. Zheng, Yanbing, 2011. "Shape restriction of the multi-dimensional Bernstein prior for density functions," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 647-651, June.
    3. Hall, Peter & Titterington, D. M., 1988. "On confidence bands in nonparametric density estimation and regression," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 228-254, October.
    4. Sonia Petrone & Piero Veronese, 2002. "Non parametric mixture priors based on an exponential random scheme," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 11(1), pages 1-20, February.
    5. Nidhan Choudhuri & Subhashis Ghosal & Anindya Roy, 2004. "Bayesian Estimation of the Spectral Density of a Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1050-1059, December.
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