IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v26y2017i2d10.1007_s10260-016-0365-8.html
   My bibliography  Save this article

On functional central limit theorems of Bayesian nonparametric priors

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-016-0365-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-016-0365-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "On the stick–breaking representation of normalized inverse Gaussian priors," DEM Working Papers Series 008, University of Pavia, Department of Economics and Management.
    2. Antonio Lijoi & Igor Pruenster, 2009. "Distributional Properties of means of Random Probability Measures," ICER Working Papers - Applied Mathematics Series 22-2009, ICER - International Centre for Economic Research.
    3. Canale, Antonio & Lijoi, Antonio & Nipoti, Bernardo & Prünster, Igor, 2023. "Inner spike and slab Bayesian nonparametric models," Econometrics and Statistics, Elsevier, vol. 27(C), pages 120-135.
    4. 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.
    5. Collet, Francesca & Leisen, Fabrizio, 2011. "Free completely random measures," DES - Working Papers. Statistics and Econometrics. WS ws112821, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Antonio Lijoi & Igor Prunster, 2009. "Models beyond the Dirichlet process," Quaderni di Dipartimento 103, University of Pavia, Department of Economics and Quantitative Methods.
    7. J. E. Griffin & M. Kolossiatis & M. F. J. Steel, 2013. "Comparing distributions by using dependent normalized random-measure mixtures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 499-529, June.
    8. Antonio Lijoi & Bernardo Nipoti & Igor Prünster, 2013. "Dependent mixture models: clustering and borrowing information," DEM Working Papers Series 046, University of Pavia, Department of Economics and Management.
    9. Lijoi, Antonio & Nipoti, Bernardo & Prünster, Igor, 2014. "Dependent mixture models: Clustering and borrowing information," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 417-433.
    10. 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.
    11. Antonio Lijoi & Igor Pruenster, 2009. "Models beyond the Dirichlet process," ICER Working Papers - Applied Mathematics Series 23-2009, ICER - International Centre for Economic Research.
    12. Federico Bassetti & Lucia Ladelli, 2021. "Mixture of Species Sampling Models," Mathematics, MDPI, vol. 9(23), pages 1-27, December.
    13. Riva Palacio, Alan & Leisen, Fabrizio, 2018. "Integrability conditions for compound random measures," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 32-37.
    14. Griffin, Jim, 2019. "Two part envelopes for rejection sampling of some completely random measures," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 36-41.
    15. Rafael Carvalho Ceregatti & Rafael Izbicki & Luis Ernesto Bueno Salasar, 2021. "WIKS: a general Bayesian nonparametric index for quantifying differences between two populations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 274-291, March.
    16. Griffin, J.E. & Steel, M.F.J., 2011. "Stick-breaking autoregressive processes," Journal of Econometrics, Elsevier, vol. 162(2), pages 383-396, June.
    17. Nieto-Barajas, Luis E., 2014. "Bayesian semiparametric analysis of short- and long-term hazard ratios with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 477-490.
    18. El-Dakkak, Omar & Peccati, Giovanni & Prünster, Igor, 2014. "Exchangeable Hoeffding decompositions over finite sets: A combinatorial characterization and counterexamples," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 51-64.
    19. Luai Al Labadi & Mahmoud Zarepour, 2018. "On Approximations of the Beta Process in Latent Feature Models: Point Processes Approach," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 59-79, February.
    20. François Caron & Emily B. Fox, 2017. "Sparse graphs using exchangeable random measures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1295-1366, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stmapp:v:26:y:2017:i:2:d:10.1007_s10260-016-0365-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.