IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v25y2016i1p113-130.html
   My bibliography  Save this article

Bayesian nonparametric location–scale–shape mixtures

Author

Listed:
  • Antonio Canale
  • Bruno Scarpa

Abstract

Discrete mixture models are one of the most successful approaches for density estimation. Under a Bayesian nonparametric framework, Dirichlet process location–scale mixture of Gaussian kernels is the golden standard, both having nice theoretical properties and computational tractability. In this paper we explore the use of the skew-normal kernel, which can naturally accommodate several degrees of skewness by the use of a third parameter. The choice of this kernel function allows us to formulate nonparametric location–scale–shape mixture prior with desirable theoretical properties and good performance in different applications. Efficient Gibbs sampling algorithms are also discussed and the performance of the methods are tested through simulations and applications to galaxy velocity and fertility data. Extensions to accommodate discrete data are also discussed. Copyright Sociedad de Estadística e Investigación Operativa 2016

Suggested Citation

  • Antonio Canale & Bruno Scarpa, 2016. "Bayesian nonparametric location–scale–shape mixtures," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 113-130, March.
    • Handle: RePEc:spr:testjl:v:25:y:2016:i:1:p:113-130
    DOI: 10.1007/s11749-015-0446-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11749-015-0446-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11749-015-0446-2?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. Lijoi, Antonio & Mena, Ramses H. & Prunster, Igor, 2005. "Hierarchical Mixture Modeling With Normalized Inverse-Gaussian Priors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1278-1291, December.
    2. David B. Dunson & Natesh Pillai & Ju‐Hyun Park, 2007. "Bayesian density regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 163-183, April.
    3. Stefano Cabras & Walter Racugno & María Eugenia Castellanos & Laura Ventura, 2012. "A Matching Prior for the Shape Parameter of the Skew-Normal Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(2), pages 236-247, June.
    4. Arellano-Valle, Reinaldo B. & Genton, Marc G. & Loschi, Rosangela H., 2009. "Shape mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 91-101, January.
    5. Pati, Debdeep & Dunson, David B. & Tokdar, Surya T., 2013. "Posterior consistency in conditional distribution estimation," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 456-472.
    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. Christian Carmona & Luis Nieto-Barajas & Antonio Canale, 2019. "Model-based approach for household clustering with mixed scale variables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(2), pages 559-583, June.
    2. Santos, Cristiano C. & Loschi, Rosangela H., 2020. "Semi-parametric Bayesian models for heterogeneous degradation data: An application to laser data," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    3. Julyan Arbel & Riccardo Corradin & Bernardo Nipoti, 2021. "Dirichlet process mixtures under affine transformations of the data," Computational Statistics, Springer, vol. 36(1), pages 577-601, March.
    4. Zahra Barzegar & Firoozeh Rivaz, 2020. "A scalable Bayesian nonparametric model for large spatio-temporal data," Computational Statistics, Springer, vol. 35(1), pages 153-173, March.

    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. Ryo Kato & Takahiro Hoshino, 2020. "Semiparametric Bayesian multiple imputation for regression models with missing mixed continuous–discrete covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 803-825, June.
    2. Debdeep Pati & David Dunson, 2014. "Bayesian nonparametric regression with varying residual density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 1-31, February.
    3. Antonio Canale & Euloge Clovis Kenne Pagui & Bruno Scarpa, 2016. "Bayesian modeling of university first-year students' grades after placement test," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(16), pages 3015-3029, December.
    4. Ryo Kato & Takahiro Hoshino, 2018. "Semiparametric Bayes Multiple Imputation for Regression Models with Missing Mixed Continuous-Discrete Covariates," Discussion Paper Series DP2018-15, Research Institute for Economics & Business Administration, Kobe University.
    5. Ryo Kato & Takahiro Hoshino, 2018. "Semiparametric Bayes Instrumental Variable Estimation with Many Weak Instruments," Discussion Paper Series DP2018-14, Research Institute for Economics & Business Administration, Kobe University.
    6. Navarrete, Carlos A. & Quintana, Fernando A., 2011. "Similarity analysis in Bayesian random partition models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 97-109, January.
    7. Corradin, Riccardo & Nieto-Barajas, Luis Enrique & Nipoti, Bernardo, 2022. "Optimal stratification of survival data via Bayesian nonparametric mixtures," Econometrics and Statistics, Elsevier, vol. 22(C), pages 17-38.
    8. Kolossiatis, M. & Griffin, J.E. & Steel, M.F.J., 2011. "Modeling overdispersion with the normalized tempered stable distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2288-2301, July.
    9. Igari, Ryosuke & Hoshino, Takahiro, 2018. "A Bayesian data combination approach for repeated durations under unobserved missing indicators: Application to interpurchase-timing in marketing," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 150-166.
    10. 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.
    11. Mitchell, James & Weale, Martin, 2019. "Forecasting with Unknown Unknowns: Censoring and Fat Tails on the Bank of England's Monetary Policy Committee," EMF Research Papers 27, Economic Modelling and Forecasting Group.
    12. Pati, Debdeep & Dunson, David B. & Tokdar, Surya T., 2013. "Posterior consistency in conditional distribution estimation," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 456-472.
    13. Antonio Lijoi & Igor Pruenster, 2009. "Models beyond the Dirichlet process," ICER Working Papers - Applied Mathematics Series 23-2009, ICER - International Centre for Economic Research.
    14. Luping Zhao & Timothy E. Hanson, 2011. "Spatially Dependent Polya Tree Modeling for Survival Data," Biometrics, The International Biometric Society, vol. 67(2), pages 391-403, June.
    15. Villani, Mattias & Kohn, Robert & Giordani, Paolo, 2009. "Regression density estimation using smooth adaptive Gaussian mixtures," Journal of Econometrics, Elsevier, vol. 153(2), pages 155-173, December.
    16. Fuentes-García, Ruth & Mena, Ramsés H. & Walker, Stephen G., 2009. "A nonparametric dependent process for Bayesian regression," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1112-1119, April.
    17. A Ford Ramsey, 2020. "Probability Distributions of Crop Yields: A Bayesian Spatial Quantile Regression Approach," American Journal of Agricultural Economics, John Wiley & Sons, vol. 102(1), pages 220-239, January.
    18. Laura Liu, 2017. "Density Forecasts in Panel Models: A semiparametric Bayesian Perspective," PIER Working Paper Archive 17-006, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 28 Apr 2017.
    19. Michael L. Pennell & David B. Dunson, 2008. "Nonparametric Bayes Testing of Changes in a Response Distribution with an Ordinal Predictor," Biometrics, The International Biometric Society, vol. 64(2), pages 413-423, June.
    20. Laura Liu, 2018. "Density Forecasts in Panel Data Models : A Semiparametric Bayesian Perspective," Finance and Economics Discussion Series 2018-036, Board of Governors of the Federal Reserve System (U.S.).

    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:testjl:v:25:y:2016:i:1:p:113-130. 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.