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On functional central limit theorems of Bayesian nonparametric priors

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  • Luai Al Labadi

    (University of Toronto)

  • Ibrahim Abdelrazeq

    (Rhodes College)

Abstract

A general approach to derive the weak convergence, when centered and rescaled, of certain Bayesian nonparametric priors is proposed. This method may be applied to a wide range of processes including, for instance, nondecreasing nonnegative pure jump Lévy processes and normalized nondecreasing nonnegative pure jump Lévy processes with known finite dimensional distributions. Examples clarifying this approach involve the beta process in latent feature models and the Dirichlet process.

Suggested Citation

  • Luai Al Labadi & Ibrahim Abdelrazeq, 2017. "On functional central limit theorems of Bayesian nonparametric priors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(2), pages 215-229, June.
    • Handle: RePEc:spr:stmapp:v:26:y:2017:i:2:d:10.1007_s10260-016-0365-8
    DOI: 10.1007/s10260-016-0365-8
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    References listed on IDEAS

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    1. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2009. "Posterior Analysis for Normalized Random Measures with Independent Increments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 76-97, March.
    2. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2006. "Conjugacy as a Distinctive Feature of the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 105-120, March.
    3. Pier Luigi Conti, 2004. "Approximated inference for the quantile function via Dirichlet processes," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 201-222.
    4. Luai Al Labadi & Mahmoud Zarepour, 2014. "Goodness-of-fit tests based on the distance between the Dirichlet process and its base measure," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 341-357, June.
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    Cited by:

    1. Luai Al-Labadi, 2021. "The two-sample problem via relative belief ratio," Computational Statistics, Springer, vol. 36(3), pages 1791-1808, September.

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